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1993 UNCO Math Contest II Problems/Problem 8

Revision as of 01:53, 20 October 2014 by Timneh (talk | contribs) (Created page with "== Problem == For what integer value of <math>n</math> is the expression <cmath>\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+\cdots +\frac...")
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Problem

For what integer value of $n$ is the expression \[\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+\cdots +\frac{1}{\sqrt{n}+\sqrt{n+1}}\] equal to $7$ ? (Hint: $(1+\sqrt{2})(1-\sqrt{2})=-1.$)


Solution

See also

1993 UNCO Math Contest II (Problems • Answer Key • Resources)
Preceded by
Problem 7 		Followed by
Problem 9
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10
All UNCO Math Contest Problems and Solutions
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