Let $$a_n = \frac{\sin(n \pi/2)}{2^n}$$ Where $a_n$ is a sequence of numbers . If $M = \max{a_n}$ and $m = \min{a_n}$ then what is the value of $M- m$ ?
My try : I found the convergence point using squeeze theorem but I'm unable to using it for computing maximum and minimum .
Edit : The previous sequence was wrong .
We have $|a_n|\leq\frac{1}{2^n}$, hence both $M=\max_{n\in\mathbb{N}}a_n$ and $m=\min_{n\in\mathbb{N}}a_n$ are attained pretty soon.
By direct inspection, $m=a_3$ and $M=a_1$.