Question

Simplify: a) (1/1 + √2) + (1/√2 + √3) + (1 /√3 + √4)
Please answer if you know.

Answer 1

I can give you the answer

Answer 2

Answer:

$\frac{1}{1 + \sqrt{2} } + \frac{1}{ \sqrt{2 } + \sqrt{3} } + \frac{1}{ \sqrt{3} + \sqrt{4} }$

$= \frac{ \sqrt{2} - 1 }{1 + \sqrt{2} ( \sqrt{2} - 1) } + \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{2} + \sqrt{3} ( \sqrt{3} + \sqrt{2)} } + \frac{ \sqrt{4} + \sqrt{3} }{ \sqrt{3} + \sqrt{4} .( \sqrt{4} - \sqrt{3)} }$

$= \frac{ \sqrt{2} - 1}{2 - 1} + \frac{ \sqrt{3} - \sqrt{2} }{3 - 2} + \frac{ \sqrt{4} - \sqrt{3} }{4 + 3}$

$= \sqrt{2} - 1 + \sqrt{3} - \sqrt{2} + \sqrt{4} - \sqrt{3}$

$= \sqrt{4} - 1$

$= 2 - 1$

$= 1$

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