1969 Canadian MO Problems/Problem 6
Problem
Find the sum of , where
.
Solution
Note that for any positive integer
Hence, pairing terms in the series will telescope most of the terms.
If is odd,
If is even,
In both cases, the expression telescopes into
1969 Canadian MO (Problems) | ||
Preceded by Problem 5 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • | Followed by Problem 7 |