Difference between revisions of "1970 Canadian MO Problems/Problem 9"

Revision as of 22:13, 27 November 2023

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 $s>t$ .

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.

@@ Line 1: / Line 1: @@
-== Problem ==
+== Problem 9 ==
+Let <math>f(n)</math> be the sum of the first <math>n</math> terms of the sequence
+<cmath> 0, 1,1, 2,2, 3,3, 4,4, 5,5, 6,6, \ldots\, .  </cmath>
+a) Give a formula for <math>f(n)</math>.
-Let <math>f(n)</math> be the sum of the first <math>n</math> terms of the sequence 0, 1,1, 2,2, 3,3, 4,4, 5,5, 6,6, \ldots\, . a) Give a formula for <math>f(n)</math>.
+b) Prove that <math>f(s+t)-f(s-t)=st</math> where <math>s</math> and <math>t</math> are positive integers and <math>s>t</math>.
-b) Prove that <math>f(s+t)-f(s-t)=s</math>t where <math>s</math> and <math>t</math> are positive integers and <math>s>t</math>.
 == Solution ==
+'''Part a):'''
+Tomas Diaz. orders@tomasdiaz.com
+{{alternate solutions}}