Question

What is the sum of the series (1/3) - (1/9) + (1/27) - ... if it converges?

a) 1/4
b) 1/6
c) 1/3
d) 1/2

Answer 1

The sum of the given series (1/3) - (1/9) + (1/27) - ... if it converges is 1/4.

Step-by-step explanation:

The given series is an alternating series where the terms alternately increase and decrease in magnitude.

To find the sum of the series, we can use the formula for the sum of an infinite geometric series:

S = a / (1 - r)

Here, a = 1/3 and r = -1/3

Plugging these values into the formula, we get:

S = (1/3) / (1 - (-1/3))

Simplifying further:

S = (1/3) / (1 + 1/3)

S = (1/3) / (4/3)

S = 1/4

Therefore, the sum of the series converges to 1/4.