Question

{X_n} converges or diverges?
\(X_n =\dfrac{(-1)^n}{n+1}\)
Help me, please

Answer 1

what is n ???
n varies from???

Answer 2

\(n\in N\)

Answer 3

loll means 1 to infinty ??

Answer 4

yes

Answer 5

\[\large -1 \le (-1)^n \le 1\]

Answer 6

\[\dfrac{-1}{n+1} \le \dfrac{ (-1)^n}{n+1} \le \dfrac{ 1}{n+1}\]

Answer 7

take the limit through out the inequality

Answer 8

yeah but -1^n will remail 1 or -1 only not between -1 and 1

Answer 9

we're setting up for using squeeze theorem here @gorv

Answer 10

It shows lim = 0--> it converges to 0
I confused at upper and lower limits
where the far left, 0 is upper limit
and the far right , 0 is upper limit, also

Answer 11

yeah that is right

Answer 12

since both upper and lower limits are 0, it converges to 0