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1970 Canadian MO Problems/Problem 9

Revision as of 23:13, 27 November 2023 by Tomasdiaz (talk | contribs)

Problem 9

Let $f(n)$ be the sum of the first $n$ terms of the sequence \[0, 1,1, 2,2, 3,3, 4,4, 5,5, 6,6, \ldots\, .\] a) Give a formula for $f(n)$.

b) Prove that $f(s+t)-f(s-t)=st$ where $s$ and $t$ are positive integers and $s>t$.

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.

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