Simplify 1/(1*2*3) + 1/(2*3*4) + 1/(3*4*5) + ... + 1/(n*(n+1)*(n+2))

Answer 1

S(1) = 1/(1*2*3) = 1/6
S(2) = 1/6 + 1/(2*3*4) = 1/6 + 1/24 = 5/24
S(3) = 5/24 + 1/(3*4*5) = 5/24 + 1/60 = 9/40

Wolfram said:

http://www.wolframalpha.com/input/?i=1%2F(1*2*3)+%2B+1%2F(2*3*4)+%2B+1%2F(3*4*5)+%2B+...+%2B+1%2F(n*(n%2B1)*(n%2B2))