Homework 5 3/16 Flow of Control

1. Project 7 of Chap. 3
輸出exponential的近似值
公式為:
1+x+x^2/2!+x^3/3!+.....+x^n/n!

程式畫面(程式碼部分)


輸出結果部分:由於篇幅過長，僅以文字呈現
請輸入x:
2
請輸入欲計算的項數n
10
2.0/1.0+
4.0/2.0+
8.0/6.0+
16.0/24.0+
32.0/120.0+
64.0/720.0+
128.0/5040.0+
256.0/40320.0+
512.0/362880.0+
1024.0/3628800.0+
=7.388994708994708
請輸入x:
2
請輸入欲計算的項數n
50
2.0/1.0+
4.0/2.0+
8.0/6.0+
16.0/24.0+
32.0/120.0+
64.0/720.0+
128.0/5040.0+
256.0/40320.0+
512.0/362880.0+
1024.0/3628800.0+
2048.0/3.99168E7+
4096.0/4.790016E8+
8192.0/6.2270208E9+
16384.0/8.71782912E10+
32768.0/1.307674368E12+
65536.0/2.0922789888E13+
131072.0/3.55687428096E14+
262144.0/6.402373705728E15+
524288.0/1.21645100408832E17+
1048576.0/2.43290200817664E18+
2097152.0/5.109094217170944E19+
4194304.0/1.1240007277776077E21+
8388608.0/2.585201673888498E22+
1.6777216E7/6.204484017332394E23+
3.3554432E7/1.5511210043330986E25+
6.7108864E7/4.0329146112660565E26+
1.34217728E8/1.0888869450418352E28+
2.68435456E8/3.0488834461171384E29+
5.36870912E8/8.841761993739701E30+
1.073741824E9/2.6525285981219103E32+
2.147483648E9/8.222838654177922E33+
4.294967296E9/2.631308369336935E35+
8.589934592E9/8.683317618811886E36+
1.7179869184E10/2.9523279903960412E38+
3.4359738368E10/1.0333147966386144E40+
6.8719476736E10/3.719933267899012E41+
1.37438953472E11/1.3763753091226343E43+
2.74877906944E11/5.23022617466601E44+
5.49755813888E11/2.0397882081197442E46+
1.099511627776E12/8.159152832478977E47+
2.199023255552E12/3.3452526613163803E49+
4.398046511104E12/1.4050061177528798E51+
8.796093022208E12/6.041526306337383E52+
1.7592186044416E13/2.6582715747884485E54+
3.5184372088832E13/1.1962222086548019E56+
7.0368744177664E13/5.5026221598120885E57+
1.40737488355328E14/2.5862324151116818E59+
2.81474976710656E14/1.2413915592536073E61+
5.62949953421312E14/6.082818640342675E62+
1.125899906842624E15/3.0414093201713376E64+
=7.389056098930649
請輸入x:
2
請輸入欲計算的項數n
100
2.0/1.0+
4.0/2.0+
8.0/6.0+
16.0/24.0+
32.0/120.0+
64.0/720.0+
128.0/5040.0+
256.0/40320.0+
512.0/362880.0+
1024.0/3628800.0+
2048.0/3.99168E7+
4096.0/4.790016E8+
8192.0/6.2270208E9+
16384.0/8.71782912E10+
32768.0/1.307674368E12+
65536.0/2.0922789888E13+
131072.0/3.55687428096E14+
262144.0/6.402373705728E15+
524288.0/1.21645100408832E17+
1048576.0/2.43290200817664E18+
2097152.0/5.109094217170944E19+
4194304.0/1.1240007277776077E21+
8388608.0/2.585201673888498E22+
1.6777216E7/6.204484017332394E23+
3.3554432E7/1.5511210043330986E25+
6.7108864E7/4.0329146112660565E26+
1.34217728E8/1.0888869450418352E28+
2.68435456E8/3.0488834461171384E29+
5.36870912E8/8.841761993739701E30+
1.073741824E9/2.6525285981219103E32+
2.147483648E9/8.222838654177922E33+
4.294967296E9/2.631308369336935E35+
8.589934592E9/8.683317618811886E36+
1.7179869184E10/2.9523279903960412E38+
3.4359738368E10/1.0333147966386144E40+
6.8719476736E10/3.719933267899012E41+
1.37438953472E11/1.3763753091226343E43+
2.74877906944E11/5.23022617466601E44+
5.49755813888E11/2.0397882081197442E46+
1.099511627776E12/8.159152832478977E47+
2.199023255552E12/3.3452526613163803E49+
4.398046511104E12/1.4050061177528798E51+
8.796093022208E12/6.041526306337383E52+
1.7592186044416E13/2.6582715747884485E54+
3.5184372088832E13/1.1962222086548019E56+
7.0368744177664E13/5.5026221598120885E57+
1.40737488355328E14/2.5862324151116818E59+
2.81474976710656E14/1.2413915592536073E61+
5.62949953421312E14/6.082818640342675E62+
1.125899906842624E15/3.0414093201713376E64+
2.251799813685248E15/1.5511187532873822E66+
4.503599627370496E15/8.065817517094388E67+
9.007199254740992E15/4.2748832840600255E69+
1.8014398509481984E16/2.308436973392414E71+
3.6028797018963968E16/1.2696403353658276E73+
7.2057594037927936E16/7.109985878048635E74+
1.44115188075855872E17/4.052691950487722E76+
2.8823037615171174E17/2.350561331282879E78+
5.7646075230342349E17/1.3868311854568986E80+
1.15292150460684698E18/8.320987112741392E81+
2.305843009213694E18/5.075802138772248E83+
4.6116860184273879E18/3.146997326038794E85+
9.223372036854776E18/1.98260831540444E87+
1.8446744073709552E19/1.2688693218588417E89+
3.6893488147419103E19/8.247650592082472E90+
7.378697629483821E19/5.443449390774431E92+
1.4757395258967641E20/3.647111091818868E94+
2.9514790517935283E20/2.4800355424368305E96+
5.9029581035870565E20/1.711224524281413E98+
1.1805916207174113E21/1.197857166996989E100+
2.3611832414348226E21/8.504785885678622E101+
4.722366482869645E21/6.123445837688608E103+
9.44473296573929E21/4.4701154615126834E105+
1.888946593147858E22/3.3078854415193856E107+
3.777893186295716E22/2.480914081139539E109+
7.555786372591432E22/1.8854947016660498E111+
1.5111572745182865E23/1.4518309202828584E113+
3.022314549036573E23/1.1324281178206295E115+
6.044629098073146E23/8.946182130782973E116+
1.2089258196146292E24/7.156945704626378E118+
2.4178516392292583E24/5.797126020747366E120+
4.8357032784585167E24/4.75364333701284E122+
9.671406556917033E24/3.945523969720657E124+
1.9342813113834067E25/3.314240134565352E126+
3.8685626227668134E25/2.8171041143805494E128+
7.737125245533627E25/2.4227095383672724E130+
1.5474250491067253E26/2.107757298379527E132+
3.0948500982134507E26/1.8548264225739836E134+
6.1897001964269014E26/1.6507955160908452E136+
1.2379400392853803E27/1.4857159644817607E138+
2.4758800785707605E27/1.3520015276784023E140+
4.951760157141521E27/1.24384140546413E142+
9.903520314283042E27/1.1567725070816409E144+
1.9807040628566084E28/1.0873661566567424E146+
3.961408125713217E28/1.0329978488239052E148+
7.922816251426434E28/9.916779348709491E149+
1.5845632502852868E29/9.619275968248206E151+
3.1691265005705735E29/9.426890448883242E153+
6.338253001141147E29/9.33262154439441E155+
1.2676506002282294E30/9.33262154439441E157+
=7.389056098930649

說明:
為求for迴圈內項目的一致性，
我們將總和的第一項"1"內定為sum的初值，
使得接下來各項的分子可固定為x^n次方
而分母則為n!
近似值即由每個迴圈的結果累加而成，
並且在迴圈尾段將分母成上x，分母乘上迴圈中的i值
供下一次計算使用。

同樣地在外部增加一個重複三次的迴圈，以方便作三個n值的計算。

2.Write a program to generate the following table of arithmetic expressions

1*1=1 1*2=2 1*3=3 ... 1*9=9
2*1=2 2*2=4 2*3=6 ... 2*9=18
...
9*1=9 9*2=18 9*3=27 ... 9*9=81

程式畫面


輸出九九乘法表，
以兩個for迴圈，控制乘數和被乘數的值，分別由1遞增到9即可。