Difference between revisions of "1970 Canadian MO Problems/Problem 9"
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'''Part a):''' | '''Part a):''' | ||
+ | <math>f(n)= | ||
+ | |||
+ | <math>f(n)=\begin{cases} \left( \frac{n-1}{2} \right)\left( \frac{n-1}{2}+1 \right),\; & n\;is\;odd \ | ||
+ | \left( \frac{n}{2} \right)\left( \frac{n}{2}+1 \right)-\frac{n}{2},\; & n\;is\;even\end{cases}</math> | ||
Revision as of 22:19, 27 November 2023
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):
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.