I have done four problems and I just want to make sure that I am doing them right before I continue.

I have to test for convergence. E= Riemann Sum :P

First problem.

infinite

E n^2/(2n^3+1)

n=1

For this i used Divergence test. Divided all terms by n^3. Ended up with 0/2. This shows that it will converge because it was 0.

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2nd problem.

Infinite

E (-1)^n (2/sqrt(n))

n=1

Bn= 2/sqrt(n) Lim n-> infinity 2/sqrt(n) = 0

Bn = 2/sqrt(n) > 2/sqrt(n+1) = B(n+1)

This shows that it converges

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3rd Problem.

Infinity

E n/2n+3

n=1

Used divergence test again.

divided all 3 terms by n

got 1/2

since not 0 it diverges

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4th problem

Infinity

E (-1)^n+1/((n^2))+3)

n=1

I did the same thing as number 2 and got the same answer.

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If there is a better way to do these, please let me know and I will redo the problem and repost it. Thank you.