For sums involving square roots like sum(1/(sqrt(k)+sqrt(k+1))): rationalize by multiplying by (sqrt(k+1)-sqrt(k))/(sqrt(k+1)-sqrt(k)). Result: sqrt(k+1)-sqrt(k) (since denominator becomes 1). Sum telescopes: sqrt(n+1)-1. Similarly, sum(1/(sqrt(k)+sqrt(k+2))) can be rationalized. For sum(sqrt(k+1)-sqrt(k)): directly telescopes to sqrt(n+1)-1. These rationalization techniques convert irrational sums into telescoping form, which is the standard JEE approach.