SOLUTION: Show that {{{1/(sqrt(a)+sqrt(a+1))}}}={{{sqrt(a+1)-sqrt(a)}}} Hence, deduce the value of {{{ 1/(sqrt(1)+sqrt(2))}}} + {{{1/(sqrt(2)+sqrt(3))}}} + {{{1/(sqrt(3)+sqrt(4))}}} + ... +

Algebra ->  Matrices-and-determiminant -> SOLUTION: Show that {{{1/(sqrt(a)+sqrt(a+1))}}}={{{sqrt(a+1)-sqrt(a)}}} Hence, deduce the value of {{{ 1/(sqrt(1)+sqrt(2))}}} + {{{1/(sqrt(2)+sqrt(3))}}} + {{{1/(sqrt(3)+sqrt(4))}}} + ... +      Log On


   

Question 225816: Show that 1%2F%28sqrt%28a%29%2Bsqrt%28a%2B1%29%29=sqrt%28a%2B1%29-sqrt%28a%29
Hence, deduce the value of +1%2F%28sqrt%281%29%2Bsqrt%282%29%29 + 1%2F%28sqrt%282%29%2Bsqrt%283%29%29 + 1%2F%28sqrt%283%29%2Bsqrt%284%29%29 + ... + 1%2F%28sqrt%288%29%2Bsqrt%289%29%29.
Please help and thanks for helping ! :D
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


First, see my lesson on Rationalizing The Denominator: http://www.algebra.com/algebra/homework/Radicals/rationalizingdenominators1.lesson

The multiplier that is necessary for this particular problem is:



Once you convert all the terms using the rule just developed, and collect like terms, you will notice that all of the terms will disappear except for -1 and , hence the sum is 2.


John