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chisigma
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From mathhelpforum.com...
$\displaystyle x=\frac{1}{\sqrt{0}+\sqrt{2}} + \frac{1}{\sqrt{2}+\sqrt{4}}+...+\frac{1}{\sqrt{2006}+\sqrt{2008}}$ (1)
... what is the value of x?...
The (1) is a telescopic sum...
$\displaystyle x=\frac{\sqrt{2}}{2} + \frac{\sqrt{4}-\sqrt{2}}{2} + \frac{\sqrt{6}-\sqrt{4}}{2}+... + \frac{\sqrt{2008}-\sqrt{2006}}{2}=\frac{\sqrt{2008}}{2}=22.405356502...$ (2)
Kind regards
$\chi$ $\sigma$
$\displaystyle x=\frac{1}{\sqrt{0}+\sqrt{2}} + \frac{1}{\sqrt{2}+\sqrt{4}}+...+\frac{1}{\sqrt{2006}+\sqrt{2008}}$ (1)
... what is the value of x?...
The (1) is a telescopic sum...
$\displaystyle x=\frac{\sqrt{2}}{2} + \frac{\sqrt{4}-\sqrt{2}}{2} + \frac{\sqrt{6}-\sqrt{4}}{2}+... + \frac{\sqrt{2008}-\sqrt{2006}}{2}=\frac{\sqrt{2008}}{2}=22.405356502...$ (2)
Kind regards
$\chi$ $\sigma$
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