An easy method?

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1 Answer
Jim H
Jan 21, 2018

Hint: #1/(sqrtn+sqrt(n+1)) = "what"#?

Explanation:

Rationalize the denominators:

#1/((sqrtn+sqrt(n+1))) * ((sqrtn - sqrt(n+1)))/((sqrtn-sqrt(n+1))) = (sqrtn-sqrt(n+1))/(n-(n+1))#

# = sqrt(n+1)-sqrtn#

So the sum above is equivalent to

#(sqrt2 - 1) + (sqrt3 - sqrt2) +(sqrt4-sqrt3) + * * * +(sqrt8-sqrt7) + (sqrt9 - sqrt 8)#
Which is #-1+sqrt9 = 2#

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