Common telescoping identities:

• 1/(k(k+1)) = 1/k - 1/(k+1) => sum = 1 - 1/(n+1) = n/(n+1)
• 1/(k(k+1)(k+2)) = (1/2)[1/(k(k+1)) - 1/((k+1)(k+2))]
• sqrt(k+1) - sqrt(k) = 1/(sqrt(k+1) + sqrt(k)) [rationalization]
• k*k! = (k+1)! - k! => sum = (n+1)! - 1