SOLUTION: Find the sum of the series 5/(sqrt2+sqrt1) + 5/(sqrt3+sqrt2) + 5/(sqrt4+sqrt3) + 5/(sqrt5+sqrt4)+...+ 5/(sqrt36)+(sqrt35)

Question 1149797: Find the sum of the series 5/(sqrt2+sqrt1) + 5/(sqrt3+sqrt2) + 5/(sqrt4+sqrt3) + 5/(sqrt5+sqrt4)+...+ 5/(sqrt36)+(sqrt35)
Answer by ikleyn(52866) (Show Source): You can put this solution on YOUR website!
.


HINT.  Multiply each denominator (and numerator) by the conjugate number to the denominator.


In each denominator, you will get the value of 1.


The numerators will form alternated sequence.


As a result, all intermediate terms will cancel each other, and you will get the combination 
of the last and the first terms as your answer.


ANSWER.  5*sqrt(36) - 5 = 5*6 - 5 = 25.

See the lesson
- Amazing calculations with fractions that contain quadratic irrationalities in denominators
in this site, Problem 4.

Your problem is solved there with all detailed explanations.

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