Difference between revisions of "1973 Canadian MO Problems/Problem 5"

Latest revision as of 17:51, 8 October 2014

For every positive integer $n$ , let $h(n) = 1+\frac{1}{2}+\frac{1}{3}+\cdots+\frac{1}{n}$ .

For example, $h(1) = 1, h(2) = 1+\frac{1}{2}, h(3) = 1+\frac{1}{2}+\frac{1}{3}$ .

Prove that $n+h(1)+h(2)+h(3)+\cdots+h(n-1) = nh(n)\qquad$ for $n=2,3,4,\ldots$

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 ==Problem==
+For every positive integer <math>n</math>, let <math>h(n) = 1+\frac{1}{2}+\frac{1}{3}+\cdots+\frac{1}{n}</math>.
+For example, <math>h(1) = 1, h(2) = 1+\frac{1}{2}, h(3) = 1+\frac{1}{2}+\frac{1}{3}</math>.
+Prove that <math>n+h(1)+h(2)+h(3)+\cdots+h(n-1) = nh(n)\qquad</math>   for   <math>n=2,3,4,\ldots</math>
 ==Solution==

1973 Canadian MO (Problems)
Preceded by Problem 4	1 • 2 • 3 • 4 • 5	Followed by Problem 6