Former profile name: i707107 Here is a list of variants of 3 problems that I solved (last edit:5/23/2017): Determine if the sequence converges: $x_0>0$, $x_1>0$, $$ x_{n+2}=frac{0.2 + x_{n+1}}{0.2 + x_n}. $$ The original problem can be found here: Determine if the series converges: $$ sum_{n=1}^{infty} frac{ sin n sin(sqrt 2 n)}n. $$ The original problem can be found here: Determine if the series converges: $$ sum_{p mathrm{prime} } frac{sin p}p. $$ The original problem can be found here: ©