MHB Which Tests Determine Convergence for These Series?

[Tebow15]

Test these for convergence.

5.
infinity
E...((n!)^2((2n)!)^2)/((n^2 + 2n)!(n + 1)!)
n = 0

6.
infinity
E...(1 - e ^ -((n^2 + 3n))/n)/(n^2)
n = 3

note: for #3: -((n^2 + 3n))/n) is all to the power of e

Btw, E means sum.

Which tests should I use to solve these?

 

[Poirot1]

Rather than posing a series of similar questions, you should apply the help given to you on one thread to attempt the other problems.

 

[Tebow15]

(Poolparty)

 

[alyafey22]

Test these for convergence.

5.
infinity
E...((n!)^2((2n)!)^2)/((n^2 + 2n)!(n + 1)!)
n = 0

6.
infinity
E...(1 - e ^ -((n^2 + 3n))/n)/(n^2)
n = 3

note: for #3: -((n^2 + 3n))/n) is all to the power of e

What do you mean by #3 ? , maybe you meant the question you posted earlier. Not writing the sums in LaTeX makes it so difficult to interpret !

 

[Ackbach]

What do you mean by #3 ? , maybe you meant the question you posted earlier. Not writing the sums in LaTeX makes it so difficult to interpret !

Moderator note: I renumbered the problems so as to have no more than two problems in a thread. The #3 should be a #6. It's Problem #6.