Close to √n

Algebra Level 2

$\large f(n) = \frac {2^{\bar n}+2^{-\bar n}}{2^n}$

Let $f(n)$ be defined as above for all positive integer $n$ , where $\bar n$ is the nearest integer to $\sqrt n$ .

What is the value of $f(1)+f(2)+f(3) + \cdots$ ?

The answer is 3.

1 solution

Alapan Das
Mar 25, 2019

If k is a positive integer such that k=ñ then k²-k+1≤n≤k²+1. Then we put the values of k and respective n s in the summation. Now, for a k, ñ=k . And n varies over the integers of the set {k²-k+1,k²+1}. As n varies from 1 to infinity k also varies from 1 to infinity. Then we get S=3

Close to √n

The answer is 3.

1 solution

0 pending reports