Find an expression for the sum of the series

[MegaDeth]

1. Homework Statement

(1x2x6) + (2x3x7) + ... + n(n + 1)(n + 5)



2. Homework Equations

Find an expression for the sum of the series. Give your answer as a product of linear factors in n.


3. The Attempt at a Solution

I haven't tried it since I don't know what to do.

 

[jedishrfu]

why don't you compute the first 5 terms of the series and see if you notice a pattern

n=1 sum=12
n=2 sum=54
n=3 ...

then divide each sum by n and see if you can find a pattern in terms of n

 

[MegaDeth]

Ok, so I have:

12/n + 42/n + 96/n + 180/n + 300/n

All I can see is that each number has a highest common denominator of 6, but I'm guessing that's not it.