InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
Find the sum of the series `1*2*3+2*3*4+3*4*5+"...." " upto n terms "` . |
|
Answer» Here, `T_(n)={" nth term of " 1,2,3,"....""}` `xx={" nth term of " 2,3,4,"...."}xx={" nth term of " 2,3,4,"...."}` ` therefore T_(n)= n(n+1)(n+2)=n^(3)+3n^(2)+2n` ` therefore S_(n)= " Sum of n terms of the series "` `sum T_(n)=sumn^(3)+3sumn^(2)+2sumn` `={(n(n+1))/(2)}^(2)+3{(n(n+1)(2n+1))/(6)}+2{(n(n+1))/(2)}` `=(n(n+1))/(2)+{(n(n+1))/(2)+(2n+1)+2}` `=(n(n+1))/(4)(n^(2)+n+4n+2+4)` `=(n(n+1)(n+2)(n+3))/(4)` |
|