Question

Calculus. Can someone check my work so far and help me finish?

Answer 1

\[\sum_{n=2}^{\infty}\frac{ 5\sqrt{n} }{ 1+n^2 }\]

Answer 2

im guessing that \[a_n= \frac{ 5n^{\frac{ 1 }{ 2 }} }{ 1+n^2 }\] and \[a_{n+1}= \frac{ 5n^{\frac{ 3 }{ 2 }} }{ 1+(n+1)^2 }\]

Answer 3

if i was correct there then\[\lim_{n \rightarrow \infty}\left| \frac{ 5n^{3/2} }{ 1+(n+1)^2 } *\frac{ 1+n^2 }{ 5n^{1/2} }\right|\]

Answer 4

this is where i get a little confused

Answer 5

\[\lim_{n \rightarrow \infty}\frac{ 5n+5n^3 }{ n^2+2n+2 }\]