Question

What is the sum of the first 10 terms of a series where (a = -16) and (r = -1/√2)?

A) (16(1 - √2))
B) (16(1 + √2))
C) (16(√2 - 1))
D) (16(√2 + 1))

Answer 1

The sum of the first 10 terms of the series is (16(1 - √2))^10.

Step-by-step explanation:

The sum of the first 10 terms of a series can be found using the formula for the sum of a geometric series:

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

Substituting the given values, we have:

S = -16(1 - (-1/√2)^10) / (1 - (-1/√2))

Simplifying this expression gives us the answer:

S = (16(1 - √2))^10)

Therefore, the sum of the first 10 terms of the series is (16(1 - √2))10.