Question

How do you use a graphing calculator to find the sum of the geometric series `Sigma 2(1/2)^(n-1)` from n=1 to 15?

Answer 1

`S_{15} =4* (1 - 1/2^15) = 3.99987792968750000000`

Explanation:

`a_0 = 2 ; q = 1/2`

`a_{14} = 2/2^14 = 2^-13`

`S_n = a_0 * frac{1 - q^n}{1-q} = a_0 + a_0 q + ... + a_0 q^{n-1}`

`S_{15} = 2* frac{1 - 0.5^15}{1-0.5}`