IIT JEE , AIEEE Forum - Mathematics , Algebra

irlmaks

I think i have a better solution

t_r+1-t_r=(4r+3)(4r+7)(4r+11)(4r+15)-(4r-1)(4r+3)(4r+7)(4r+11)

=16(4r+3)(4r+7)(4r+11)

=16t_r /4r-1

implies 19t_r+t_r+1=4r.t_r+1- 4(r-1)t_r

telescoping we get 4n.t_n+1-4.0(t₁)=20S_n+t_n+1-t₁

hence S_n=[(4n-1)(4n+3)(4n+7)(4n+11)(4n+15)+3.7.11.15]/20

DONT HESITATE TO ASK FOR ELOBERATION OF MY SOLUTION IF U THINK MY SOLUTION IS OVER ELAGENT