Which of the following statements is correct? (a) [? (n=1) to ?] (sin(n))/(n^2)

Question

Which of the following statements is correct? (a) [? (n=1) to ?] (sin(n))/(n^2) converges, and [? (n=1) to ?] (2n)/((n^4)-3) converges. (b) [? (n=1) to ?] (sin(n))/(n^2) diverges, and [? (n=1) to ?] (2n)/((n^4)-3) diverges. (c) [? (n=1) to ?] (sin(n))/(n^2) converges, and [? (n=1) to ?] (2n)/((n^4)-3) diverges. (d) [? (n=1) to ?] (sin(n))/(n^2) diverges, and [? (n=1) to ?] (2n)/((n^4)-3) converges. (e) [? (n=1) to ?] (sin(n))/(n^2) converges, and [? (n=1) to ?] (2n^4)/((n^4)-3) converges. The last choice (e) is different than the rest!

Explanation / Answer

(b) [? (n=1) to ?] (sin(n))/(n^2) diverges, and [? (n=1) to ?] (2n)/((n^4)-3) diverges.

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