Question

Let the series 𝑆 and 𝑇 be defined by
$∑^∞_{n-0}\frac{ 2 ⋅ 5 ⋅ 8 ⋯ (3𝑛 + 2) }{1 ⋅ 5 ⋅ 9 ⋯ (4𝑛 + 1)}$ and $∑^∞ _{n=1}(1 + \frac{1 }{𝑛} ) ^{−𝑛^2}$
respectively. Then, which one of the following statements is TRUE?

• A. 𝑆 is convergent and 𝑇 is divergen
• B. 𝑆 is divergent and 𝑇 is convergent
• C. Both 𝑆 and 𝑇 are convergent
• D. Both 𝑆 and 𝑇 are divergent

Answer 1

Answer: (C)

Both 𝑆 and 𝑇 are convergent

Answer 2

The correct option is (C): Both 𝑆 and 𝑇 are convergent