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

(Created page with "== Problem == 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 wh...")
 
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== Problem ==
 
== Problem ==
  
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).  
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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 f(s+t)-f(s-t)=st where s and t are positive integers and s>t.  
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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 ==
 
== Solution ==

Latest revision as of 13:02, 11 March 2019

Problem

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

Solution

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