Question

Test the series for convergence or divergence. Say if convergence is conditional \[\sum_{2}^{\infty}\left( \left( -1 \right)^{n +1}n \right)\div \left( 4n ^{2}+1 \right)\]

Answer 1

its the sum from one to infty sorry \[\sum_{1}^{\infty}\]

Answer 2

The series converges by the alternating series test (to around 0.129032) but does not converge absolutely by the integral test.