1970 Canadian MO Problems/Problem 9
Problem 9
Let be the sum of the first terms of the sequence a) Give a formula for .
b) Prove that where and are positive integers and .
Solution
Part a):
Using in the formula we can have:
Therefore,
Part b):
since , then and our expression reduces to:
Tomas Diaz. orders@tomasdiaz.com
Alternate solutions are always welcome. If you have a different, elegant solution to this problem, please add it to this page.