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Set up a spreadsheet to compute exp x up to say the 100th
term using your series.
Solution:
What I would do is to put the value of x (which you can specify
as you wish) in b1. (and the symbol x in a1)
Then I would put j in column A starting with 0 in a2. (Put
=a2+1 in a3 and copy it down) ; put x in column B (set =b1+1
in b2 and copy it down); put 
in column C (set c2 to =1 and c3 to = c2*b3/a3) and but the
"partial sum to the jth term" in column D (set d2=d1+c2
and copy it down)
Setting x = 1 here is what I get
|
x
|
1
|
|
|
|
0
|
=B1
|
1
|
=D1+C2
|
|
=A2+1
|
=B2
|
=C2*B3/A3
|
=D2+C3
|
|
=A3+1
|
=B3
|
=C3*B4/A4
|
=D3+C4
|
|
=A4+1
|
=B4
|
=C4*B5/A5
|
=D4+C5
|
|
=A5+1
|
=B5
|
=C5*B6/A6
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=D5+C6
|
|
=A6+1
|
=B6
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=C6*B7/A7
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=D6+C7
|
|
=A7+1
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=B7
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=C7*B8/A8
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=D7+C8
|
|
=A8+1
|
=B8
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=C8*B9/A9
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=D8+C9
|
|
=A9+1
|
=B9
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=C9*B10/A10
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=D9+C10
|
|
=A10+1
|
=B10
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=C10*B11/A11
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=D10+C11
|
|
=A11+1
|
=B11
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=C11*B12/A12
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=D11+C12
|
|
=A12+1
|
=B12
|
=C12*B13/A13
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=D12+C13
|
|
=A13+1
|
=B13
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=C13*B14/A14
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=D13+C14
|
The results are
|
x
|
1
|
|
|
|
0
|
1
|
1
|
1
|
|
1
|
1
|
1
|
2
|
|
2
|
1
|
0.5
|
2.5
|
|
3
|
1
|
0.1667
|
2.666666667
|
|
4
|
1
|
0.0417
|
2.708333333
|
|
5
|
1
|
0.0083
|
2.716666667
|
|
6
|
1
|
0.0014
|
2.718055556
|
|
7
|
1
|
0.0002
|
2.718253968
|
|
8
|
1
|
2E-05
|
2.71827877
|
|
9
|
1
|
3E-06
|
2.718281526
|
|
10
|
1
|
3E-07
|
2.718281801
|
|
11
|
1
|
3E-08
|
2.718281826
|
|
12
|
1
|
2E-09
|
2.718281828
|
|
13
|
1
|
2E-10
|
2.718281828
|
|
14
|
1
|
1E-11
|
2.718281828
|
|
15
|
1
|
8E-13
|
2.718281828
|
Additional Exercise: for x=5 which is the largest term
in the series? For x = 10? In general?
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