Problem 10

Suppose are positive real numbers satisfying for all If k is any integer, find the sum in terms of n only (the sum turns out to be independent of k)

.

[Problem submitted by Iris Magee, LACC Instructor of Mathematics.]

Solution:

Let stand for the sum: = .

Now rewrite the sum in reverse order: =

We were given that . This implies

So, .

Add the first two equations to get

2= Therefore, .