1962 AHSME Problems/Problem 40
The limiting sum of the infinite series, whose th term is is:
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
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.
Problem starts at 2:20 : https://www.youtube.com/watch?v=3PDZtddYQoM&t=5s