Question

If $b_n$ is changed as $b_1=1$, $b_n=b_{n-1}+\cos b_{n-1}$ then the sequence $\left\{b_n\right\}$ is

• A. Increasing
• B. decreasing
• C. Neither increasing nor decreasing
• D. Not bounded.

Answer 1

The correct option is C Neither increasing nor decreasing

$b_n=b_{n-1}+\cos b_{n-1}$
We have $b_2=1+\cos b_1$
$\Rightarrow$ $b_2>b_1$ and $b_3=1+\cos b_2<1+\cos b_1=b_2$
$\Rightarrow$ $b_3<b_2$
$\therefore$ Sequence $\left\{b_n\right\}$ is non monotonic

Hence neither increasing nor decreasing.