# Thread: sum of the series

1. ## sum of the series

I am asked to use this formula: Sn = a/1-r for |r|<1 To solve this problem:
(1.07) + (1.07)^2 + (1.07)^3 + ...+(1.07)^60
I was trying to think of this in terms of sigma notation where we have a lower and upper limit and then raising it to a power to get the sum. I can see the exponent changing from 0 to 60 and a common ratio of (1.07). I tried putting it into the calculator as sum(seq(1.07x,x,0,60) =1958.1 but I am not sure how that helps me. I guess I am a little lost, could someone put me in the right direction.
Thank you,
Keith Stevens

2. Hello, Keith!

I am asked to use this formula: Sn = a/(1-r) for |r|<1 to solve this problem:
. . (1.07) + (1.07)^2 + (1.07)^3 + ...+(1.07)^60
Wrong formula!

That formula is for an infinite geometric series.
. . This series is not infinite; it has only 61 terms.

For a geometric series with n terms, the formula is:

. . . . . . . . . . . 1 - r^n
. . . S_n . = . a --------
. . . . . . . . . . . . 1 - r

3. There is an additional problem with kcsteven's formula that I think is important to mention. To use S = a/(1-r), we require that |r| < 1, whereas in his series r = 1.07.

-Dan