Proove that 1/root2+1 1/root3+root2+1/root4+1/root5+root5,=root5-1
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1/(1 + √2) + 1/(√2 + √3) + 1/(√3 + √4) + 1/(√4 + √5) + 1/(√5 + √6) + 1/(√6 + √7) + 1/(√7 + √8) + 1/(√8 + √9)
Rationalizing each term
1/(1 + √2) = ((√2- 1))/((√2+ 1) (√2- 1) ) = ((√2- 1))/((〖√2〗^2- 1)) = √2-1
We will get similar result like above for all the terms
= √2 – 1 + √3 - √2 + √4 - √3+ √5 - √4 + √6 - √5 + √7 - √6 + √8 - √7 + √9 - √8
=√9 – 1
=3 – 1
= 2
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2 IS UR ANSWER DEAR...★✰✯★✰✯☢︎︎☼︎✯★✰༆༄߷☢︎︎
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