Question

Prove that 1/1+root2 + 1/root2 + root3 + 1/ root3+ root4.......1/root 8 +root 3 = 2

Answer 1

Step-by-step explanation:

$\\ \\ the \: correct \: question \: is \: \\ \frac{1}{1 + \sqrt{2} } + \frac{1}{ \sqrt{2} + \sqrt{3} } + \frac{1}{ \sqrt{3} + \sqrt{4} } + ...... + \frac{1}{ \sqrt{8} + \sqrt{9} }$

ANSWER

$\\ \frac{1}{1 + \sqrt{2} } + \frac{1}{ \sqrt{2} + \sqrt{3} } + \frac{1}{ \sqrt{3} + \sqrt{4} } + ...... + \frac{1}{ \sqrt{8} + \sqrt{9} }$

the above question proceed by first step you rationalize all fractional irrational number.

i.e,

$\\ \frac{1}{1 + \sqrt{2} } + \frac{1}{ \sqrt{2} + \sqrt{3} } + \frac{1}{ \sqrt{3} + \sqrt{4} } + ...... + \frac{1}{ \sqrt{8} + \sqrt{9} } \\ \\ 3 - 1 = 2$

Hence ,

LHS = RHS