By induction for all n ∈ N \(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+....+\frac{1}{n(n+1)(n+2)}\) is equal to:-
1
\(\frac{n(n+7)}{8(n+1)(n+2)}\)
2
\(\frac{n(n+9)}{10(n+1)(n+2)}\)
3
\(\frac{n(n+5)}{6(n+1)(n+2)}\)
4
\(\frac{n(n+3)}{4(n+1)(n+2)}\)
5
Not Attempted