Question

Prove the following theorem

Answer 1

consider a series \[\sum_{i=1}^{\infty} a_n \]

Answer 2

if \[\lim_{n \rightarrow \infty}\] \[(2n+1)|a_(n+1)|/|a_n|=L < 1 then a series \sum_{i=1}^{\infty} a_n converges\]

Answer 3

lets assume that \[\lim_{n \rightarrow \infty} (2n+1)|a_n+1| /|a_n|=L<1 \] then for any \[\epsilon>0\] it is possible to find \[N(\epsilon)\] such that for all