Question

Use an appropriate comparison test to determine the convergence/divergence of the following series:

a.)∑ n= (1)/(√n−1) (Upper limit of the sigma is ∞ and the lower limit of the sigma is n=2)

b.) ∑ n=n(n+1)/(n^2+1) (n-1) (Upper limit of sigma is ∞ and the lower limit of sigma is n=2)

c.) ∑ n= cos^2(n)/ (n^3/2) (Upper limit of sigma is ∞ and the lower limit of sigma is n=1)

d.) ∑ 5^n/(√n4^n) (Upper limit of sigma is ∞ and the lower limit of sigma is n=1)

e.) ∑ n (1)/(In(In(n))) (Upper limit of sigma is ∞ and the lower limit of the sigma is n=3)

f.) ∑ (n+2^n)/(n^2*2^n) (Upper limit of sigma is ∞ and the lower limit of the sigma is n=1)

g.) ∑ (1)/(1^2+2^2+ 3^2+...+n^2) (Upper limit of sigma is ∞ and the lower limit of the sigma is n=1)

Answer 1