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提问：级别：二年级来自：安徽省合肥市
回答数：2浏览数：
已知全集U={1，2，3，4，5，6，7，8}，A={x|x2-3x+2=0},B={x|1≤x≤5
已知全集U={1，2，3，4，5，6，7，8}，A={x|x2-3x+2=0},B={x|1≤x≤5,x属于Z}C={x|2&x&9,x属于Z}
求A∪（B∩C）
求（CUB）∪（CUC）.
请尽量给出过程
&提问时间： 16:53:33
最佳答案此答案已被选择为最佳答案，但并不代表问吧支持或赞同其观点
回答：级别：高二 12:32:34来自：河南省平顶山市
先解方程得到：A={1,2}，根据后面范围得B={1,2,3,4,5}，C={3,4,5,6,7,8}
然后就知道A∪（B∩C）=={1,2}∪{3,4,5}={1,2,3,4,5}，
第二个式子可以先变形，利用性质得到={1，2，6，7，8}
提问者对答案的评价：
回答：级别：高级教员 17:32:21来自：山东省临沂市
由题意可知A={1,2}
B={1,2,3,4,5}
C={3,4,5,6,7,8}
所以B∩C={3,4,5}
所以A∪（B∩C）={1,2,3,4,5}
CUB={6,7,8}
所以（CUB）∪（CUC）={1，2，6，7，8}
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Can anyone help please? I need to know how to make the sum of value S(n) = 0+1+2+3+4...+(n-1)+n (example: 0+1+2+3 = 6 , 0+1+2+3+4+5+6+7 = 28 and so on) on Latex
110k9193389
The difficult task is generating the terms of the sequence, not computing the sum, I present a macro that prints all the terms or just the sum. You can define a different starting point and another difference (defaults 0 and 1).
\documentclass{article}
\usepackage{xparse}
\ExplSyntaxOn
\NewDocumentCommand{\arithmeticsequence}{sO{}m}
\group_begin:
\keys_set:nn {rudstep/arseq} { #2 }
\IfBooleanTF{#1}
{ \rudstep_arseq_sum:n { #3 } }
{ \rudstep_arseq_full:n { #3 } }
\group_end:
\keys_define:nn { rudstep/arseq }
.int_set:N = \l_rudstep_diff_int,
start .int_set:N = \l_rudstep_start_int,
.initial:n = 1,
start .initial:n = 0,
\seq_new:N \l_rudstep_terms_seq
\cs_new_protected:Npn \rudstep_arseq_full:n #1
\seq_clear:N \l_rudstep_terms_seq
\int_step_inline:nnnn
{ \l_rudstep_start_int } % start
{ \l_rudstep_diff_int }
{ \l_rudstep_start_int + #1*\l_rudstep_diff_int }
{ \seq_put_right:Nn \l_rudstep_terms_seq { ##1 } }
$\seq_use:Nn \l_rudstep_terms_seq { + } = \rudstep_arseq_sum:n { #1 }$
\cs_new:Npn \rudstep_arseq_sum:n #1
\int_eval:n { (#1+1)*(2*\l_rudstep_start_int+#1*\l_rudstep_diff_int)/2 }
\ExplSyntaxOff
\begin{document}
Just the sum of five terms after 0: \arithmeticsequence*{5}
The whole sequence: \arithmeticsequence{3}
Or: \arithmeticsequence{4}
Start from 1: \arithmeticsequence[start=1]{3}
A big example:
\arithmeticsequence[start=81297,diff=198]{180}
\end{document}
Of course, if you know how to do it in Lisp, then here's the way:
\documentclass{article}
\usepackage{lisp-on-tex}
\begin{document}
\lispinterp{
(\define \intsum
(\lambda (\n)
(\lispif (\= \n :0 ) :0
(\+ (\intsum (\- \n :1)) \n))))}
\lispinterp{(\texprint(\intsum:100))}
\end{document}
that prints, as is well known,
Note: shamelessly adapted from the documentation of lisp-on-tex.
The e-TeX version of the same idea, using recursion, can be
\documentclass{article}
\newcommand{\Sn}[1]{%
\number\numexpr #1
\ifnum\numexpr#1-1&0
+\expandafter\Sn\expandafter{\number\numexpr#1-1}
\begin{document}
\end{document}
Note that this is fully expandable. The macro \Sn starts from the argument and if it's bigger than 1 asks to expand \Sn with the argument decreased by 1. One might start also from 0, but I'll leave it as an exercise to the interested reader.
494k5613312346
\documentclass{article}
\newcommand\foo[1]{\the\numexpr((#1)*(#1+1))/2\relax}
% or if you want to print the terms
\newcommand\foob[1]{$\fooc{#1}{0}=\foo{#1}$}
\newcommand\fooc[2]{\the\numexpr#2\relax\ifnum#1=#2\relax\else+\fooc{#1}{\numexpr#2+1\relax}\fi}
\begin{document}
\foo{8} and \foo{5}
\foob{8} and \foob{5}
\end{document}
333k267971407
Using Lua is probably a huge overkill in this situation, but it shows off how one can easily integrate Lua in LaTeX.
The code might also be easier to grasp for programmers who are beginners in LaTeX ;)
% !TEX TS-program = lualatex
% !TEX encoding = UTF-8 Unicode
\documentclass{article}
\usepackage[utf8]{luainputenc}
\usepackage{luacode}
% The code won't work as-is if you move it into \directlua{}.
% If you do so, be sure to replace "~" (in i ~= startInt) by \string~
\begin{luacode}
function calcSum(startInt, endInt)
local sum = 0
for i=startInt, endInt do
sum = sum + i
return sum
function writeSum(startInt, endInt)
local sum = 0
local tex = ""
for i=startInt, endInt do
if i ~= startInt then
tex = tex .. " + "
sum = sum + i
tex = tex .. i
tex = tex .. " = " .. sum
return tex
\end{luacode}
\def\calcSum#1#2{\directlua{
tex.print(calcSum(tonumber(#1), tonumber(#2)))
\def\writeSum#1#2{\directlua{
tex.print(writeSum(tonumber(#1), tonumber(#2)))
\begin{document}
The sum of the numbers \(0, 1, 2, \ldots, 28\) is \(\calcSum{0}{28}\).\\
Another sum: \(\writeSum{100}{103}\).
\end{document}
Here is a short expl3 approach using \int_step_inline:nnnn. This carries out the explicit sum and doesn't rely on Gauss' reduction. So this is for illustration purposes only.
\documentclass{article}
\usepackage{xparse}
\ExplSyntaxOn
\cs_generate_variant:Nn \int_to_arabic:n { V }
\cs_new:Npn \rudstep_sum:n #1
\int_zero:N \l_tmpa_int
\int_step_inline:nnnn { 1 } { 1 } { #1 }
\int_add:Nn \l_tmpa_int { ##1 }
\int_to_arabic:V \l_tmpa_int
\NewDocumentCommand \calcsum {m}
\rudstep_sum:n { #1 }
\ExplSyntaxOff
\begin{document}
\calcsum{8}
\end{document}
27.2k365146
Using my package calculator, you can perform arithmetic calculations comfortably. This code solves your problem:
\documentclass{article}
\usepackage{ifthen}
\usepackage{calculator}
\newcounter{n}
\newcommand{\sumZeroToN}[2]{%
\COPY{0}{#2}
\whiledo{\not{\value{n}&#1}}{%
\ADD{#2}{\value{n}}{#2}\stepcounter{n}}}
\begin{document}
\sumZeroToN{100}{\sol}
\sum_{n=0}^{100} n = \sol
\end{document}
An expandable solution using the package
for computations and \xintiloop for expandably looping with an index.
\documentclass{article}
\usepackage{bnumexpr}% minimally extends \numexpr to big integers (new on CTAN
% for \xintiloop: (for fun)
\usepackage{xinttools}% automatically loaded by xint, which is loaded by
% bnumexpr, but in the future bnumexpr will only load a
% smaller part of xint, and xint itself will not load
% xinttools anymore.
\newcommand{\ArithmeticSequenceAndItsSum}[3]{%
% #1= initial term, A
% #2= common difference, d
% #3= number of terms, N
% sum is A+(A+d)+...+(A+(N-1)d)=N*A+d*N(N-1)/2
% (cf. Gauss Werke, Kindergarten Abteilung)
#1% assume N at least one and that #1 does not need to be evaluated
\xintiloop [1+1]
\unless\ifnum#3=\xintiloopindex
+\thebnumexpr#1+\xintiloopindex*#2\relax
=\thebnumexpr #3*#1+#2*#3*(#3-1)/2\relax
\begin{document}
$\ArithmeticSequenceAndItsSum {0}{1}{10}$
$\ArithmeticSequenceAndItsSum {1}{2}{10}$
\noindent $\ArithmeticSequenceAndItsSum {}{}{100}$
And now go see the log for some bigger integers!!
\message{\ArithmeticSequenceAndItsSum {}{}{1000}}
\end{document}
29.4k46101
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TeX - LaTeX Stack Exchange works best with JavaScript enabled4.7+2.3=4.5×2=6.9-2.5=7.2×0.8=6×3.4=0.62-0.32=1.4×0.5=0.75×100=0.02×0.5=3.6÷0.3=6.3÷7=5.6÷100=0.75÷0.25=0.125×8=4.8÷0.3=0.96÷2=0.56÷28=0.36÷0.4=0.64÷0.8=0.72÷3.6=3.6÷24=0.8×1.1=7.2+12.8=46.7-3.8=12.8÷4=5.2÷13=12.5÷5=1.64÷41=10÷20=24÷15=8.65×10=0.35×0.6=3.08×0.01=4.95××0.1=0.4×0.5=2.4÷0.8=10.8÷9=9.6÷0.8=0.108÷2=4.95÷0.9=9.65÷0.1=0.325×100=2.5×8=0.56÷0.7=0.125×4=3.28×0.1=3.9÷0.13=7.2×0.1=0.01×0.1=0.25×0.4=1.6÷0.8=1÷2.5=1.25×0.8=3.2÷0.04=0÷1.7=0.22×102=9.6÷0.8=5×0.24=4.5-0.05=3.9÷0..5=5×0.12=24×0.5=4.8×0.5=2.8+4.2=0.84÷2.1=5÷0.25=7.8÷0.01=5.4÷0.6=3.2÷5=7×0.62=0.56÷0.8=7.4-2.8=0.18÷0.2=0.16÷8=4.5×0.02=8+7.2=1.2×30=0.012×0.2=7.3×0.3=9÷6=3.6÷0.12=7.8÷0.6=2÷5=4.5+5=0.3÷0.6=0.96÷0.2=10.5×0.4=7.3+0.27=8×0.125=0.54÷0.6=0.61+0.39=0.56÷28=10÷20=4.08÷0.4=11-9.4=0.8×0.11=0.72+12.8=5.6÷0.01=2.3×100=0.75×100=0.108÷2=10.8÷9=0.7÷0.8=16-5.07=4.2×0.4=0.72×6=12÷0.5=5.2×0.4=12.2÷0.2=5.6÷100=0.41+3.7=0.02×0.5=7.2-0.8=1.4×0.5=84÷0.21=0.75÷0.25=2.5×16=0.108÷2=1.75+32.5=16-5.07=5.2÷13=1.64÷41=1.02×0.2=0.26×0.3=8.4×0.02=1.29×6=0.8×0.05=12.6÷0.03=8.71÷0.1=21÷0.21=0.8×0.13=0.34÷17=8.08÷0.4=0.5×2.2=1.24÷4=3.27+0.63=5.02×0.3=0.3×0.5=6.4÷4=7.2÷1.8=0.7÷0.35=0.72÷1.44=0.48÷0.04=1.25÷2.5=5.5+55=16.8÷8=0.54+2.2=3.5-0.05=2÷0.02=0.25×40=1.5×0.6=0.32÷0.8=12.25÷0.5=73.5×0.1=46.5+52.5=0.45×102=1.25×88=2.64+3.85+1.54=8×1.25=5.6÷3.5=4.2÷0.7÷6=0.4×8.6×25=0.27÷0.3=2.5×101=0.65×101-0.65=2.6×7÷2.6×7= - 跟谁学
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在线咨询您好，告诉我您想学什么，15分钟为您匹配优质老师哦马上咨询&&&分类：4.7+2.3=4.5×2=6.9-2.5=7.2×0.8=6×3.4=0.62-0.32=1.4×0.5=0.75×100=0.02×0.5=3.6÷0.3=6.3÷7=5.6÷100=0.75÷0.25=0.125×8=4.8÷0.3=0.96÷2=0.56÷28=0.36÷0.4=0.64÷0.8=0.72÷3.6=3.6÷24=0.8×1.1=7.2+12.8=46.7-3.8=12.8÷4=5.2÷13=12.5÷5=1.64÷41=10÷20=24÷15=8.65×10=0.35×0.6=3.08×0.01=4.95××0.1=0.4×0.5=2.4÷0.8=10.8÷9=9.6÷0.8=0.108÷2=4.95÷0.9=9.65÷0.1=0.325×100=2.5×8=0.56÷0.7=0.125×4=3.28×0.1=3.9÷0.13=7.2×0.1=0.01×0.1=0.25×0.4=1.6÷0.8=1÷2.5=1.25×0.8=3.2÷0.04=0÷1.7=0.22×102=9.6÷0.8=5×0.24=4.5-0.05=3.9÷0..5=5×0.12=24×0.5=4.8×0.5=2.8+4.2=0.84÷2.1=5÷0.25=7.8÷0.01=5.4÷0.6=3.2÷5=7×0.62=0.56÷0.8=7.4-2.8=0.18÷0.2=0.16÷8=4.5×0.02=8+7.2=1.2×30=0.012×0.2=7.3×0.3=9÷6=3.6÷0.12=7.8÷0.6=2÷5=4.5+5=0.3÷0.6=0.96÷0.2=10.5×0.4=7.3+0.27=8×0.125=0.54÷0.6=0.61+0.39=0.56÷28=10÷20=4.08÷0.4=11-9.4=0.8×0.11=0.72+12.8=5.6÷0.01=2.3×100=0.75×100=0.108÷2=10.8÷9=0.7÷0.8=16-5.07=4.2×0.4=0.72×6=12÷0.5=5.2×0.4=12.2÷0.2=5.6÷100=0.41+3.7=0.02×0.5=7.2-0.8=1.4×0.5=84÷0.21=0.75÷0.25=2.5×16=0.108÷2=1.75+32.5=16-5.07=5.2÷13=1.64÷41=1.02×0.2=0.26×0.3=8.4×0.02=1.29×6=0.8×0.05=12.6÷0.03=8.71÷0.1=21÷0.21=0.8×0.13=0.34÷17=8.08÷0.4=0.5×2.2=1.24÷4=3.27+0.63=5.02×0.3=0.3×0.5=6.4÷4=7.2÷1.8=0.7÷0.35=0.72÷1.44=0.48÷0.04=1.25÷2.5=5.5+55=16.8÷8=0.54+2.2=3.5-0.05=2÷0.02=0.25×40=1.5×0.6=0.32÷0.8=12.25÷0.5=73.5×0.1=46.5+52.5=0.45×102=1.25×88=2.64+3.85+1.54=8×1.25=5.6÷3.5=4.2÷0.7÷6=0.4×8.6×25=0.27÷0.3=2.5×101=0.65×101-0.65=2.6×7÷2.6×7=4.7+2.3=4.5×2=6.9-2.5=7.2×0.8=6×3.4=0.62-0.32=1.4×0.5=0.75×100=0.02×0.5=3.6÷0.3=6.3÷7=5.6÷100=0.75÷0.25=0.125×8=4.8÷0.3=0.96÷2=0.56÷28=0.36÷0.4=0.64÷0.8=0.72÷3.6=3.6÷24=0.8×1.1=7.2+12.8=46.7-3.8=12.8÷4=5.2÷13=12.5÷5=1.64÷41=10÷20=24÷15=8.65×10=0.35×0.6=3.08×0.01=4.95×1000=6.9×0.1=0.4×0.5=2.4÷0.8=10.8÷9=9.6÷0.8=0.108÷2=4.95÷0.9=9.65÷0.1=0.325×100=2.5×8=0.56÷0.7=0.125×4=3.28×0.1=3.9÷0.13=7.2×0.1=0.01×0.1=0.25×0.4=1.6÷0.8=1÷2.5=1.25×0.8=3.2÷0.04=0÷1.7=0.22×102=9.6÷0.8=5×0.24=4.5-0.05=3.9÷0.1316.5÷0.5=5×0.12=24×0.5=4.8×0.5=2.8+4.2=0.84÷2.1=5÷0.25=7.8÷0.01=5.4÷0.6=3.2÷5=7×0.62=0.56÷0.8=7.4-2.8=0.18÷0.2=0.16÷8=4.5×0.02=8+7.2=1.2×30=0.012×0.2=7.3×0.3=9÷6=3.6÷0.12=7.8÷0.6=2÷5=4.5+5=0.3÷0.6=0.96÷0.2=10.5×0.4=7.3+0.27=8×0.125=0.54÷0.6=0.61+0.39=0.56÷28=10÷20=4.08÷0.4=11-9.4=0.8×0.11=0.72+12.8=5.6÷0.01=2.3×100=0.75×100=0.108÷2=10.8÷9=0.7÷0.8=16-5.07=4.2×0.4=0.72×6=12÷0.5=5.2×0.4=12.2÷0.2=5.6÷100=0.41+3.7=0.02×0.5=7.2-0.8=1.4×0.5=84÷0.21=0.75÷0.25=2.5×16=0.108÷2=1.75+32.5=16-5.07=5.2÷13=1.64÷41=1.02×0.2=0.26×0.3=8.4×0.02=1.29×6=0.8×0.05=12.6÷0.03=8.71÷0.1=21÷0.21=0.8×0.13=0.34÷17=8.08÷0.4=0.5×2.2=1.24÷4=3.27+0.63=5.02×0.3=0.3×0.5=6.4÷4=7.2÷1.8=0.7÷0.35=0.72÷1.44=0.48÷0.04=1.25÷2.5=5.5+55=16.8÷8=0.54+2.2=3.5-0.05=2÷0.02=0.25×40=1.5×0.6=0.32÷0.8=12.25÷0.5=73.5×0.1=46.5+52.5=0.45×102=1.25×88=2.64+3.85+1.54=8×1.25=5.6÷3.5=4.2÷0.7÷6=0.4×8.6×25=0.27÷0.3=2.5×101=0.65×101-0.65=2.6×7÷2.6×7=科目:最佳答案4.7+2.3=74.5×2=96.9-2.5=4.47.2×0.8=5.766×3.4=20.40.62-0.32=0.31.4×0.5=0.70.75×100=750.02×0.5=0.013.6÷0.3=126.3÷7=0.95.6÷100=0.0560.75÷0.25=30.125×8=14.8÷0.3=160.96÷2=0.480.56÷28=0.020.36÷0.4=0.90.64÷0.8=0.80.72÷3.6=0.23.6÷24=0.150.8×1.1=0.887.2+12.8=2046.7-3.8=42.912.8÷4=3.25.2÷13=0.412.5÷5=2.51.64÷41=0.0410÷20=0.524÷15=1.68.65×10=86.50.35×0.6=0.213.08×0.01=0.03084.95×6.9×0.1=0.690.4×0.5=0.22.4÷0.8=310.8÷9=1.29.6÷0.8=120.108÷2=0.0544.95÷0.9=5.59.65÷0.1=96.50.325×100=32.52.5×8=200.56÷0.7=0.80.125×4=0.53.28×0.1=0.3283.9÷0.13=307.2×0.1=0.720.01×0.1=0.0010.25×0.4=0.11.6÷0.8=21÷2.5=0.41.25×0.8=13.2÷0.04=800÷1.7=00.22×102=22.449.6÷0.8=125×0.24=1.24.5-0.05=4.453.9÷0.13=3016.5÷0.5=335×0.12=0.624×0.5=124.8×0.5=2.42.8+4.2=70.84÷2.1=0.45÷0.25=207.8÷0.01=7805.4÷0.6=93.2÷5=0.647×0.62=4.340.56÷0.8=0.77.4-2.8=4.60.18÷0.2=0.90.16÷8=0.024.5×0.02=0.098+7.2=15.21.2×30=360.012×0.2=0.00247.3×0.3=2.199÷6=1.53.6÷0.12=307.8÷0.6=132÷5=0.44.5+5=9.50.3÷0.6=0.50.96÷0.2=4.810.5×0.4=4.27.3+0.27=7.578×0.125=10.54÷0.6=0.90.61+0.39=10.56÷28=0.0210÷20=0.54.08÷0.4=10.211-9.4=1.60.8×0.11=0.0880.72+12.8=13.525.6÷0.01=5602.3×100=2300.75×100=750.108÷2=0.05410.8÷9=1.20.7÷0.8=0.87516-5.07=10.934.2×0.4=1.680.72×6=4.3212÷0.5=245.2×0.4=2.0812.2÷0.2=615.6÷100=0.0560.41+3.7=4.110.02×0.5=0.017.2-0.8=6.41.4×0.5=0.784÷0.21=4000.75÷0.25=32.5×16=400.108÷2=0.0541.75+32.5=34.2516-5.07=10.935.2÷13=0.41.64÷41=0.041.02×0.2=0.2040.26×0.3=0.0788.4×0.02=0.1681.29×6=7.740.8×0.05=0.0412.6÷0.03=4208.71÷0.1=87.121÷0.21=1000.8×0.13=0.1040.34÷17=0.028.08÷0.4=20.20.5×2.2=1.11.24÷4=0.313.27+0.63=3.95.02×0.3=1.5060.3×0.5=0.156.4÷4=1.67.2÷1.8=40.7÷0.35=20.72÷1.44=0.50.48÷0.04=121.25÷2.5=0.55.5+55=60.516.8÷8=2.10.54+2.2=2.743.5-0.05=3.452÷0.02=1000.25×40=101.5×0.6=0.90.32÷0.8=0.412.25÷0.5=24.573.5×0.1=7.3546.5+52.5=990.45×102=45.91.25×88=1102.64+3.85+1.54=8.038×1.25=105.6÷3.5=1.64.2÷0.7÷6=10.4×8.6×25=8.60.27÷0.3=0.92.5×101=252.50.65×101-0.65=652.6×7÷2.6×7=49解析
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