# 1962 AHSME Problems/Problem 40

## Problem

The limiting sum of the infinite series, whose th term is is:

## Solution

The series can be written as the following:

and so on.

by using the formula for infinite geometric series ,

We can get ... Since they all have common denominators, we get . Using the infinite series formula again, we get

## Solution 2

So.. we have the sum to be ... Notice that this can be written as . Now, it is trivial that the new fraction we seek is

Testing the answer choices, we see that is the correct answer.

## Solution 3

Let Then Subtracting from , we got: Therefore, the answer is . -nullptr07

## Video Solution

Problem starts at 2:20 : https://www.youtube.com/watch?v=3PDZtddYQoM&t=5s