Question

Evaluate the geometric series

Answer 1

Answer:

Option B is correct.

sum of given geometric series is, 255

Step-by-step 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:

$S_n = \frac{a(r^n-1)}{r-1}$ 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,

$\frac{2}{1} = 2$

$\frac{4}{2} = 2$ and so on...

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

$S_n = \frac{1((2)^8-1)}{2-1}$

or

$S_n = 256-1 = 255$

Therefore, the sum of given geometric series is, 255

Answer 2

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