1962 AHSME Problems/Problem 40
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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 Now, testing the answer choices, we see that is the correct answer.