Find the sum 1/(sqrt(2) + sqrt(1)) + 1/(sqrt(3) + sqrt(2)) + 1/(sqrt(4) + sqrt(3)) + ... + 1/(sqrt(25) + sqrt(24)).
+128474 1 1 1 1
________ + ______ + _______ + ...... .+ _________
√2 + √1 √3 +√2 √4 + √3 √25 + √24
Multiply numerator/denominator of each fraction by the conjugate of its denominator and we get that
√2 -√1 √3 - √2 √4 - √3 √25 - √24
______ + ______ + _______ + ...... + __________ =
1 1 1 1
- √1 + ( √2 - √2) + ( √3 - √3) + ( √4 - √4) + ......+ (√24 - √24) + √25 =
√25 - √1 =
5 - 1 =
4
