Question

Convergence

Answer 1

Can someone tell my whether this series are divergent, conditional convergence or abs convergence
\[\sum_{n=1}^{∞}\frac{ n+(-1)^n7 }{ 2^n+1 }\]

Answer 2

*me

Answer 3

Hints:
1. split the sum into two by splitting the numerator (optional)
2. use the ratio test, find the limit of \( r=\frac{a_{n+1}}{a_n} \).
If \( r\rightarrow 0\) as \( n\rightarrow \infty\), then series is convergent.
Also, if \( r=\frac{|a_{n+1}|}{|a_n|} \rightarrow 0\) as \( n\rightarrow \infty\), then series is absolutely convergent convergent.

Answer 4

Thank you

Answer 5

you're welcome!