Homework Help: Sequence Question

1. The problem statement, all variables and given/known data
U( r ) = r(r+1)(r+2)(r+3), show that U (r + 1) - U ( r ) = 4(r+1)(r+2)(r+3) Hence, find the sum to n terms of the series 2x3x4 + 3x4x5 + 4x5x6 +.....



2. Relevant equations

Sequence Knowledge..

3. The attempt at a solution

I can't even TOUCH on the problem. Can you please help?

 

U( r ) = r(r+1)(r+2)(r+3), show that U (r + 1) - U ( r ) = 4(r+1)(r+2)(r+3)

U(r+1) is = (r+1)(r+2)(r+3)(r+4)

so U(r+1) - U( r ) = (r+1)(r+2)(r+3)(r+4) - r(r+1)(r+2)(r+3)

let (r+1)(r+2)(r+3) = z

= z((r+4)-r)

= 4z

= 4(r+1)(r+2)(r+3)



Then if we say V(r) = U(r+1) - U( r )

V(r) + V(r + 1) = U(r+1) - U(r) + U(r+2) - U(r+1)

= U(r+2) - U(r)

Then we're finding 1/4 of Summation of V(r) so

Summation of 0.25V(r) = 0.25 U(r+n) - U(r)

?? is this it?

oh yeah and where did the 1/4 come from?