Question

examine the convergence of the following series
sigma n=1 upto infinity (n/3n+1)^n

Answer 1

Answer:

S(n) = 1/3 +2/3^2+3/3^3 +4/3^4 +. , ,+

(1/3)S. 1/3^2+2/3^3+3/3^4+. +

(2/3)S(n) =1/3 +1/3^2 +1/3^3+1/3^4+. ,, ,,,+,

(2/3)S(n) = (1/3)/[1- (1/3)] = (1/3)/(2/3) = 1/2

(2/3)S(n) = (1/2)

S(n) = 3/4

Answer 2

Answer:

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