Question

state convergent or divergent if convergent find the sum justify all answers mathematically

(n+1)/(2n+5) n=1 to infinity

Answer 1

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

Using the limit test, if
\[\lim_{n\rightarrow\infty}\frac{n+1}{2n+5} \neq 0\]
the series is divergent, if it does equal 0 we don't know if it's convergent yet.

\[\lim_{n\rightarrow\infty}\frac{n+1}{2n+5} = \lim_{n\rightarrow\infty}\frac{1+\frac{1}{n}}{2+\frac{5}{n}} = \frac{1}{2}\]

Since \[\lim_{n\rightarrow\infty}\frac{n + 1}{2n + 5} \neq 0 \]
the series is divergent

Answer 2

THat Awesome Meepi thank you!