Find the sum of n terms of the series is 1*2*3*+2*3*4+3*4*5+.....

Answers (1)

Solution:    We have ,

                      S_n=1cdot 2cdot 3+2cdot 3cdot 4+3cdot 4cdot 5+.............

                    We know ,    S_n=sum_n=1^nT_n=sum_n=1^nn(n+1)(n+2)

                   Rightarrow                    S_n=sum_n=1^nn^3+3sum_n=1^nn^2+2sum_n=1^nn

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

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