What do u mean? The exercise wants me to prove that this series converges... (It's n factorial. There is no m)

sum n!*ln^n(1+2/n) Sent from my Redmi Note 4X using Tapatalk

to domy7997, you have very poor penmanship. Those are clearly

*m's* in the image you posted.

It may serve better if you used some devise other than a mobile phone.

Also be reminded that this is an English language website.

Now just to be sure that the series is: \(\displaystyle \sum\limits_{n = 1}^\infty {n!{{\left[ {\log \left( {1 + \frac{2}{n}} \right)} \right]}^n}} \)

If that is correct then the ratio test is a better way to prove convergence.