Question

Evaluate:
10
Σ 4(2)n-1
n = 1
S = [?]

Answer 1

S = 4,092

Explanation:

to evaluate the sum:

Σ [4(2)^(n-1)] from n = 1 to 10

use the formula for the sum of a geometric series:

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

in this case, a = 4(2)^(1-1) = 4(2)^0 = 4, and r = 2.

now, plug these values into the formula and find the sum:

S = 4 * (1 - 2^10) / (1 - 2)

S = 4 * (1 - 1024) / (-1)

S = 4 * (-1023) / (-1)

S = 4 * 1023

S = 4 * 1023

S = 4,092

the sum of the series is 4,092.