Math problem lol

[BFM_Fénix]

Hey, i recently finished the semester (yeah!!!!!!!!) but i have a question: can anyone solve this?

_infinity
S ^(n+2)!(n)2/_n!(n²-1)
ⁿ⁼¹

_infinity
S ^(-1)n(x)2n+1/_(2n+1)!
ⁿ⁼¹

They are mathematical series problems. any comment will be precciated  
*I think both are easy  *

 

UPS, forgot something. Say if the series converge or diverge. If converge please give me the result. GL i honestly hope someone will know this, have fate in u

[Goalie]

Top one will diverge, bottom one will converge.

That's all I can help with.  If I had some more time, I would try and solve it, but i don't right now.  Maybe one of our resident mathmaticians can help you.

[BFM_Edison]

First diverges and second converges to sin(x) - x. Second one is the taylor series for sin(x) without the x term, hence the sin(x) - x.

[Haunted]

*looks at jim*

[UCANTSEEME]

*looks at jim*

and

*scratches his head*

[BFM_Fénix]

Thx for giving the rigth answer, it was a debate with a friend of mine. He didnt believe me those were the real answers (maybe because i never went to math class or the ! played with his mind lol)

[jim360]

*looks at jim*

Since Edison's answer looks right (and for the second one is exactly right) I can't see the reason to post myself.

Applying D'alambert's ratio test to the first series is enough to show that it diverges since as n tends to infinity a_n+1/a_n tends to 1+O(1/n) which is greater than 1.

[Haunted]

*looks at jim*

Since Edison's answer looks right (and for the second one is exactly right) I can't see the reason to post myself.

and he posts anyway  the spammer.. lol

[BFM_Edison]

*looks at jim*

Since Edison's answer looks right (and for the second one is exactly right) I can't see the reason to post myself.

Applying D'alambert's ratio test to the first series is enough to show that it diverges since as n tends to infinity a_n+1/a_n tends to 1+O(1/n) which is greater than 1.

I concur.

Who's the spammer now I'm concurring with an agreement with my answer

[Haunted]

lol