Infinite Summation Math Portfolio

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Example Math Portfolio SL

Infinite Summation - Type 1:

We being this analysis by investigating series of the type , where tn represents the nth term in the series, x and a are two parameters that may be varied and n! = n X (n -1) X (n -2) X ... X 3 X 2 X 1.

Initially we will consider the summation, Sn where Sn means to sum the first n terms of the series. We will find the Sn for the first 11 summations of this series, that is those terms that obey .

Using Microsoft Excel we can easily obtain these values which are shown in the table below.

N

Sn

0

1

1

1.693147

2

1.933374

3

1.988878

4

1.998496

5

1.999829

6

1.999983

7

1.999999

8

2

9

2

10

2

To further clarify how these values were obtained a sample calculation is shown below:

, a screenshot highlighting the formula used in Excel to complete the rest is shown in figure 1 below.