Real Analysis I need a detailed, rigorous proof for the following and I may not use the comparison test. I need to prove this series convergent using other properties of convergent series, if Sn the...

Real Analysis

I need a detailed, rigorous proof for the following and I may not use the comparison test.  I need to prove this series convergent using other properties of convergent series,  if Sn the sequence of partial sums is increasing and bounded then Sn is convergent and therefore the Series is convergent.  Below is the Series that I must prove convergent.

Prove that 1+1/2! + 1/4! + 1/6! + . . . converges.

I am thinking that this will become 1/(2n-2)!

Perhaps use the principle of mathematical induction?

Thank you