# Thread: Difficulty writing the summation notation..

1. ## Difficulty writing the summation notation..

I'm having some difficulty writing the geometric summation notation of this question:

3. a) write the series 10 + 5 + 5/2 + 5/4 + 5/8 + 5/16 + 5/32 using summation notation (sigma).

I discovered each term is divided by 2 so in this case r= 1/2

The formula Sn = [a(r^n-1)] / (r-1) should be this:

S1 = [10 (1/2^2 - 1)] / (1/2 - 1)

However, when I then try to verify this formula I get 10 when n=1 but 15 when n=2.

I must be doing something wrong, but I don't know what. I will give this another crack and see if I can find my errors. Any help is appreciated.

2. Hi

You made one simple mistake only:

The geometric sum is indeed $S_n = \frac{a(r^n-1)}{r-1}$ but this only applies when |r| > 1

When |r| < 1, it's actually $S_n = \frac{a(1-r^n)}{1-r}$

I can show you proof of this if you like.