Question

Evaluate the geometric series

Answer 1

sum = (2^8 - 1)/(2-1)=256-1=255

Answer 2

Option B is correct.

sum of given geometric series is, 255

Explanation:

Evaluate the geometric series:
`\sum_(i=1)^(8) 2^(i-1)`

we can write this as:

`1+2+4+.......+128`

Formula for the sum of the geometric series:

`S_n = (a(r^n-1))/(r-1)` for r > 1

where

a is the first term

n is the number of terms

r is the common ratio

In the given series:

common ratio (r) = 2>1, n = 8 and first term(a) = 1

Since,

`(2)/(1) = 2`

`(4)/(2) = 2` and so on...

then substitute the given values in [1] we have;

`S_n = (1((2)^8-1))/(2-1)`

or

`S_n = 256-1 = 255`

Therefore, the sum of given geometric series is, 255