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). | + | 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)= | + | 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 == | ||
Revision as of 13:02, 11 March 2019
Problem
Let 
be the sum of the first 
terms of the sequence 0, 1,1, 2,2, 3,3, 4,4, 5,5, 6,6, \ldots\, . a) Give a formula for .
b) Prove that 
t where 
and 
are positive integers and 
.
