[quote=Juancd08;337083]SUM(arctan(a_n) converges if and only if SUM(a_n) converges.

preposition

1.Let arctan(a_n)=b_n => tan(b_n)=a_n

2.ıf any sequence is converges than its subsequences also converge.

Solution

tan(b_n) is a subsequence of b_n. By the comparison princeple if b_n is converge then tan b_n also converge. Conversly now show that if tan(b_n) is converge than b_n converges. Similiarly arctan(a_n) is subsequence of a_n then right handed also satisfies. then proof is done