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(1)/(1+√(2) ) +(1)/(√(2) +√(3) ) +...+(1)/(√(99) +√(100) )
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(1)/(1+√(2) ) +(1)/(√(2) +√(3) ) +...+(1)/(√(99) +√(100) )

User Doge
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1 Answer

15 votes
15 votes

Answer:

9

Explanation:

the given expression can be re-written:


(√(2) -1)/((√(2)-1)(√(2)+1)) +(√(3) -√(2))/((√(3) +√(2))(√(3) -√(2))) + ...+(√(100) -√(99))/((√(100) -√(99))(√(100) +√(99)));

then


√(2) -1+√(3) -√(2) +√(4) -√(3)+√(5) -√(4)+...+√(100)-√(99)= -1+√(100)=9.

User Palto
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