# Solution for finding the sum of an infinite sequence

Internal Assessment 1

Solution for finding the sum of a infinite sequence

The objective of this assignment is to find out the sum of infinite sequences , where

In this equation,  is defined by the term number. For example,  is the first term, whereas  is the nth term.  are various variables. In this equation,  which is defined by . Likewise 3! is defined by 3, but there is an exception

First I will break down the equation so that it will be easier for me to find out he formula. I will examine the  defined as the sum of the first . For example, , . I am first going to use this equation , where , , and where  is . So it should look like this:

I will find out the  for .

In order to find , I used my TI-84 Plus to figure this out. I will plug in the equation                  , where the  is 1,  is 2 and  value is from 0 to 10. The method is shown in the appendix.

I came up with:

In order to check if I got it right, I used Microsoft Excel 2010. The method is shown in the appendix.

After seeing that my result matches the results in Excel, I decided to then find out the sum. I found out the sum using my TI-84 Plus. The method is shown in the appendix.

This is what I did in order to get  for .

I got 1 because of .

Here  is equal to  plus  because  is the sum of the pervious             term. So if I add  which is term number 1, it will give me the . I will use this formula  to find out the sum’s up to n = 10.

Now, we can sub as 1 and  as

Here n = 2, so

I did this for  where

On the other hand, I used Microsoft Excel 2010 to do it for me too. ...