Determine whether the series
∞
E (-1)^n+1 (n+3)/(n +10)
j=1

converges absolutely, converges conditionally, or diverges, showing all work

Question

Determine whether the series 
  ∞
E     (-1)^n+1 (n+3)/(n +10)
j=1                

converges absolutely, converges conditionally, or diverges, showing all work

anonymous · Answer

For a series
$$
\sum_1^\infty a_n

$$
to convege, then
$$
\lim a_n=0
$$
Do we violate this with the given series

anonymous · Answer

With the given series
$$
a_n=(-1)^{n+1} \frac {n+3}{n+10}\

|a_n|= \frac {n+3}{n+10}\
$$
What is the llimit
$$
\lim_{n\to \infty}  \frac {n+3}{n+10}
$$

anonymous · Answer

The limit is 1, so $a_n$ does not go to zero and the series diverges.

anonymous · Answer

do u get it

anonymous · Answer

Thanks, @eliassaab  and thanks for checkin' @prowrestler