Question

What is the sum of the geometric series 0.25,0.5,1,2,…,256?

A) 255.75
B) 512
C) 1023
D) 2047

Answer 1

The sum of the geometric series 0.25, 0.5, 1, 2,..., 256 is 127.75.

Step-by-step explanation:

To find the sum of a geometric series, we can use the formula:

S = a(1 - r^n) / (1 - r)

where S is the sum, a is the first term, r is the common ratio, and n is the number of terms. In this case, the first term (a) is 0.25, the common ratio (r) is 2, and the number of terms (n) is 9. Substituting these values into the formula, we get:

S = 0.25(1 - 2^9) / (1 - 2) = 0.25(-511) / (-1) = 127.75

So, the sum of the geometric series is 127.75.