Question

What is the sum of this geometric series. `sum2(3)^( n-1)` for n=1 to 6?

Answer 1

`728`

Explanation:

Since

`a+ar+ar^2+cdots+ar^(n-1)=(a(1-r^n))/(1-r)`,

we have

`sum_{n=1}^6 2(3)^(n-1)=(2(1-3^6))/(1-3)=728`

I hope that this was clear.