- #1
mindauggas
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Homework Statement
(1) [itex]\frac{1}{(1+x^{2})}[/itex]+[itex]\frac{1}{(1+x^{2})^{2}}[/itex]+...+[itex]\frac{1}{(1+x^{2})^{n}}[/itex]
The Attempt at a Solution
(2) [itex]\frac{1}{(1+x^{2})}[/itex]*[itex]\frac{(1+x^{2})^{n-1}}{(1+x^{2})^{n-1}}[/itex]+[itex]\frac{1}{(1+x^{2})^{2}}[/itex]*[itex]\frac{(1+x^{2})^{n-2}}{(1+x^{2})^{n-2}}[/itex]+...+[itex]\frac{1}{(1+x^{2})^{n}}[/itex]*[itex]\frac{(1+x^{2})^{n-n}}{(1+x^{2})^{n-n}}[/itex]
(3) [itex]\frac{(1+x^{2})^{n-1}+(1+x^{2})^{n-2}+...+(1+x^{2})^{n-n}}{(1+x^{2})^{n}}[/itex]
Then I use the formula
[itex]{S(n)=\frac{n(n-1)}{2}}[/itex]
I think i didn't do (2) correctly (reduction to a common denominator). Or did I?
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