(−1)^n n^2÷(n(n+1))
My answer is that the sequence and series both diverge because they both alternate between 1 and -1 on a graph. But taking the limit of the sequence gives me "1".

Question

(−1)^n n^2÷(n(n+1))
My answer is that the sequence and series both diverge because they both alternate between 1 and -1 on a graph.  But taking the limit of the sequence gives me "1".

experimentx · Answer

the sequence neither converge nor diverge because it's an alternating sequence.

experimentx · Answer

the series does not converge because the limit of nth term as n->infinity is not zero.

anonymous · Answer

So I cant use any other test to see if it conv. or diverges. And u said that it neither conv or dive. Can I say that they are "inconclusive"?

experimentx · Answer

well, as far I have known, (-1)^n neither converges or diverges, rather it is sated as undefined.
$$ lim_{n->\inf}\frac{(−1)^n n^2}{(n(n+1))} $$ seems rather undefined.

anonymous · Answer

Think the same way. Since this is part of my project i just want to make sure. And honestly, Im supposed to graph and just tell if they conv. or div.

anonymous · Answer

**I think the same way**

experimentx · Answer

the sequence seems that it does not converge or diverge (it's an oscillating sequecne)

the series seems to diverge.

experimentx · Answer

wolfram says it does not converge, and it fails convergence test, so it menas it should diverge

anonymous · Answer

Ok, thank you!

experimentx · Answer

yw