Friday, March 19, 2021

Consider this expression

 For any positive integer m 



2 comments:

Kirtivasan Ganesan said...

According to me 1/(n(n+1)) converges. However 1/(n(n+k)) diverges where k is any positive integer other than 1.
Wolfram alpha says 1/(n(n+k)) converges for any positive integer value of k including 1.
Wolfram alpha doesn't accept Gauss constant G. I accept whole heartedly Gauss constant G.
These two are what I don't agree with Wolfram alpha. I have reasonable knowledge to oppose and state my viewpoint.

Kirtivasan Ganesan said...

I learnt the comparison test of convergence.
1/(n(n+1+(k-1))) is also convergent by comparison test, if 1/(n(n+1)) is convergent. That clears one issue with Wolfram alpha.
I must say sorry on the Gauss issue because I have learnt a lot from Internet/Wikipedia/Wolfram Alpha.
This finishes the argument.