CALCULUS Series Problem (Converge or Diverge)

Hi I would like to ask for the proper code for this problem. I'm new to this software so I still don't know how to properly type the code. Thank you!

Answer 1

[Walter Roberson]

syms n
symsum(n/(2*n+1),n,1,inf)

You should be able to prove the result easily. When n becomes large enough, the +1 becomes relatively unimportant, so the ratio approaches n/(2*n) which approaches 1/2 . The sum of an infinite number of values that are nearly 1/2 going to be infinite.

Answer 2

[Deepak]

syms n

symsum(n/(2*n+1),n,1,inf)

[Walter Roberson]

please explain the difference between this answer and the one I gave several years ago?