Using the Limit Comparison Test with ∑n=1∞1n2\sum_{n=1}^{\infty} \frac{1}{n^2}∑n=1∞n21, determine the convergence of ∑n=1∞n3+2nn5−n2+1\sum_{n=1}^{\infty} \frac{n^3 + 2n}{n^5 - n^2 + 1}∑n=1∞n5−n2+1n3+2n.
The series converges because the limit comparison ratio is 1 and the comparison series converges
The series diverges because the limit comparison ratio is ∞\infty∞
The series converges because the limit comparison ratio is 12\frac{1}{2}21 and the comparison series converges
The Limit Comparison Test is inconclusive here