Common telescoping identities:

• $\frac{1}{k(k+1}$) = 1/k - $\frac{1}{k+1}$ => sum = 1 - $\frac{1}{n+1}$ = $\frac{n}{n+1}$
• $\frac{1}{k(k+1}$(k+2)) = $\frac{1}{2}$[$\frac{1}{k(k+1}$) - $\frac{1}{(k+1}$(k+2))]
• sqrt(k+1) - sqrt(k) = $\frac{1}{sqrt(k+1}$ + sqrt(k)) [rationalization]
• k*k! = (k+1)! - k! => sum = (n+1)! - 1