You made one simple mistake only:
The geometric sum is indeed but this only applies when |r| > 1
When |r| < 1, it's actually
I can show you proof of this if you like.
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.