Does the series converge or diverge? if it converges, what is the sum? show your work.

∑∞n=1−4(−1/2)n−1

my guess is s=-2 2/3

Step-by-step explanation:

The series is an infinite one. It starts at n = 1

Givens

k= - 4  

n = 1

a = (-1/2)^(1 - 1)

a = 1

r = -1/2

Formula

Sum = k*a/(1 - r) Forget the k for the moment and just work on a/(1 - r)

Solution

Sum = k [1 / (1 - - 1/2) ]

Sum = k [1 / (3/2)]

Sum = k [2/3]

Sum = k 0.666666666

Now we can deal with the 4

Sum = -4 * 2/3 = -8/3 = -2 2/3 which is exactly what you had.

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step-by-step explanation: