Question

Determine whether the series converges or diverges. If it converges, find its sum. State which test you used. 4-3+9/4-27/16+

Answer 1

Answer: It converges to 16/7

Step-by-step explanation

The first four terms of the series are

4, -3, 9/4, -27/16

Divide each term over its previous term to find the common ratio is r = -3/4. This shows we have a geometric series. Since -1 < r < 1 is the case, the infinite sum converges to S = a/(1-r) where 'a' is the first term.

So,

S = a/(1-r)

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

S = 4/(1 + 3/4)

S = 4/(4/4 + 3/4)

S = 4/(7/4)

S = 4*(4/7)

S = 16/7