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]  

Most Viewed Questions

Preparation Products

Knockout CUET (Physics, Chemistry and Mathematics)

Complete Study Material based on Class 12th Syllabus, 10000+ Question Bank, Unlimited Chapter-Wise and Subject-Wise Mock Tests, Study Improvement Plan.

₹ 7999/- ₹ 4999/-
Buy Now
Knockout CUET (Physics, Chemistry and Biology)

Complete Study Material based on Class 12th Syllabus, 10000+ Question Bank, Unlimited Chapter-Wise and Subject-Wise Mock Tests, Study Improvement Plan.

₹ 7999/- ₹ 4999/-
Buy Now
Knockout JEE Main (Six Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 9999/- ₹ 8499/-
Buy Now
Knockout JEE Main (Nine Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 13999/- ₹ 12499/-
Buy Now
Knockout NEET (Six Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 9999/- ₹ 8499/-
Buy Now
Boost your Preparation for JEE Main with our Foundation Course
 
Exams
Articles
Questions