Answer Find a formula for the nth partial sum of the series, 2 - 2/3 + 2/9 - 2/2

Question

Answer

Find a formula for the nth partial sum of the series, 2 - 2/3 + 2/9 - 2/27 + middot middot middot + (-1)n-1 2/3n - 1 + and use it to find the series' sum if the series converges. The formula for the nth partial sum, sn of the series is . If the series is convergent, what is the series' sum? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. The series is convergent, and the sum is . (Type an integer or a simplified fraction.) The series diverges.

Explanation / Answer

s_n = 2(1-(-1/3)^n)/(1-(-1/3)) = (3/2)(1-(-1/3)^n) The series converges to 2/(1+1/3) = 3/2

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