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Infinite Serieshard
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Apply the Integral Test to ∑n=2∞n(n2+1)ln⁡(n2+1)\sum_{n=2}^{\infty} \frac{n}{(n^2+1) \ln(n^2+1)}∑n=2∞​(n2+1)ln(n2+1)n​. Evaluate the improper integral ∫2∞x dx(x2+1)ln⁡(x2+1)\int_2^{\infty} \frac{x \, dx}{(x^2+1) \ln(x^2+1)}∫2∞​(x2+1)ln(x2+1)xdx​ and determine convergence.