Determine with limitrules if following sequence convergence, if yes then calculate its limit

$$b_n := \left\{
\begin{array}{l l}
\frac{1+n}{n} & \quad \text{falls $n$ is odd }\
\frac{1-n}{n} & \quad \text{if $n$ is even}\
\end{array} \right.$$

for $$n\geq 1$$

Question

Determine with limitrules if following sequence convergence, if yes then calculate its limit

$$b_n := \left\{ 
  \begin{array}{l l}
    \frac{1+n}{n} & \quad \text{falls $n$ is odd }\
    \frac{1-n}{n} & \quad \text{if $n$ is even}\
  \end{array} \right.$$

for $$n\geq 1$$

anonymous · Answer

No convergence since for odd b_n = 1 + 1/n ---> 1
and for even b_n = 1/n - 1 ---> -1

anonymous · Answer

As u know 1/n ---> 0

anonymous · Answer

Soo solved.

anonymous · Answer

ok thanks, you mean its enough in exam, when i write like you wrote here ??

anonymous · Answer

BTW sequence must have the same limit for every sub-sequence it has if the full sequence has a limit. Here 2 sub-sequences have 2 DIFFERENT limits ==> NO convergence

anonymous · Answer

Add the last remark, and click "close question"