Let the series S and T be defined by S = sumn=0^infty 2cdot 5cdot 8 cdots (3n+2)/1cdot 5cdot 9 cdots (4n+1)quadandquad T = sumn=1^infty (1+1/n)^-n^2, respectively. Then, which one of the following statements is TRUE?

(C) Both S and T are convergent

Q25Section A (Section A)25 of 60

Ratio and root test for series

Let the series $S$ and $T$ be defined by $S = \sum_{n=0}^\infty \frac{2\cdot 5\cdot 8 \cdots (3n+2)}{1\cdot 5\cdot 9 \cdots (4n+1)}\quad\text{and}\quad T = \sum_{n=1}^\infty \left(1+\frac{1}{n}\right)^{-n^2},$ respectively. Then, which one of the following statements is TRUE?

Pick an option to check your answer.

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