Does summation of 1/n converge or diverge?

Example: Test for convergence the series ) Solution : () We know log n < n for all n 2 2 1 n logn 1 (ii) n-2 logn 1 Vn22 logn n 11 or n logn Vn 2. Since diverges, so by First Comparison Test, diverges. n-2log n 1 1 We knoW n logn n (ii) Vn2 3. converges, so by First Comparison Test, ; 1 Since -2n logn Converges EYamnle Test for the converqence of the series