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Find the exact value of the sum of n0 to infinity of n13nSol

Find the exact value of the sum of n=0 to infinity of (n+1)/(3^n)

Solution

n=0 xn+1 = x/(1-x)

Differentiate:

n=0 (n+1)xn = 1/(1-x)2

Therefore:

n=0 (n+1)(1/3)n = 1/(1-1/3)2 = 1/(4/9) = 9/4 = 2.25

Find the exact value of the sum of n=0 to infinity of (n+1)/(3^n)Solutionn=0 xn+1 = x/(1-x) Differentiate: n=0 (n+1)xn = 1/(1-x)2 Therefore: n=0 (n+1)(1/3)n = 1

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