]> Exercise 2.2

Exercise 2.2

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 x j j ! in column C (set c2 to =1 and c3 to = c2*b3/a3) and but the "partial sum to the j-th 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

=D5+C6

=A6+1

=B6

=C6*B7/A7

=D6+C7

=A7+1

=B7

=C7*B8/A8

=D7+C8

=A8+1

=B8

=C8*B9/A9

=D8+C9

=A9+1

=B9

=C9*B10/A10

=D9+C10

=A10+1

=B10

=C10*B11/A11

=D10+C11

=A11+1

=B11

=C11*B12/A12

=D11+C12

=A12+1

=B12

=C12*B13/A13

=D12+C13

=A13+1

=B13

=C13*B14/A14

=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?