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convergence of series

Source: LIMIT 2019 CCS2 P3

April 28, 2021
seriesalgebraSummation

Problem Statement

Which of the following series are convergent? <spanclass=′latex−bold′>(A)</span> ∑n=1∞2n2+35n3+1<span class='latex-bold'>(A)</span>~\sum_{n=1}^\infty\sqrt{\frac{2n^2+3}{5n^3+1}} <spanclass=′latex−bold′>(B)</span> ∑n=1∞(n+1)nnn+3/2<span class='latex-bold'>(B)</span>~\sum_{n=1}^\infty\frac{(n+1)^n}{n^{n+3/2}} <spanclass=′latex−bold′>(C)</span> ∑n=1∞n2x(1−x2)n<span class='latex-bold'>(C)</span>~\sum_{n=1}^\infty n^2x\left(1-x^2\right)^n <spanclass=′latex−bold′>(D)</span> None of the above<span class='latex-bold'>(D)</span>~\text{None of the above}
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