Addition

Question

1 / 1+  root(2)    +       1 /root(2) + root(3)     +  1/ root(3) + root(4)   + ....................................1 / root(15) + root(16)  is ??

Answer 1

$=>\frac{1}{\sqrt{1}+\sqrt{2}} + \frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}} + .........+\frac{1}{\sqrt{15}+\sqrt{16}}\\
=>\frac{1}{\sqrt{2}+\sqrt{1}} * \frac{\sqrt{2}-\sqrt{1}}{\sqrt{2}- \sqrt{1}} +\frac{1}{\sqrt{3}+\sqrt{2}} *  \frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}-\sqrt{2}}.......
\frac{1}{\sqrt{16}+\sqrt{15}} *\frac{\sqrt{16}-\sqrt{15}}{\sqrt{16}-\sqrt{15}}.\\
=\sqrt{16}-\sqrt{1} \\
=4-1 = 3

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