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

asked Oct 1, 2022 58.5k views

1 vote

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4 votes

Answer:

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.

Exclsr answered Oct 7, 2022

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