# Infinite series convergence III

#### cacophony

##### New member
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?

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#### Poirot

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

#### ZaidAlyafey

##### Well-known member
MHB Math Helper
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

##### Indicium Physicus
Staff member
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.