Find the value of1.2.3+2.3.4+3.4.5+...to n terms= ?

Answers (1)

Solution: Let T_n be the nth term of the given series .Then

                    T_n=n(n+1)(n+2)

                      T_n=n^3+3n^2+2n

           Let  S_n denote the sum of nth terms of the given series .then

           Rightarrow    S_n=sum_k=1^nT_k=sum_k=1^n(n^3+3n^2+2n)

        Rightarrow    S_n=[fracn(n+1)2]^2+3[fracn(n+1)(2n+1)6]+2[fracn(n+1)2]  

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