# SL IA Type 1: Infinite Summation Portfolio

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.

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.

Figure 1: Showing how Excel was used to calculate Sn

If we now take these values and create a graph of n vs. Sn we obtain the result shown in Figure 2

From this graph it is clearly seen that the summation Sn converges on ...