Hi,
I'm having a bit of trouble with understanding geometric series and was wondering if someone can help me out?
E.g 1 + 2 + 4 + 8 + ... 2^k
The answer is 2^(k + 1) - 1, can someone help explain why that is?
I can see the pattern: 2^0, 2^1, 2^2, ...
So to get the n = 3 term, then 2^3-1 = 2^2 = 4 --> which would be 2^k-1. But why is is k+1? Also where did the minus 1 come from at the end?
Thanks!
I'm having a bit of trouble with understanding geometric series and was wondering if someone can help me out?
E.g 1 + 2 + 4 + 8 + ... 2^k
The answer is 2^(k + 1) - 1, can someone help explain why that is?
I can see the pattern: 2^0, 2^1, 2^2, ...
So to get the n = 3 term, then 2^3-1 = 2^2 = 4 --> which would be 2^k-1. But why is is k+1? Also where did the minus 1 come from at the end?
Thanks!