# Inf Series, Summations with k, k^2 to get Summation of k(k+1)

1. Nov 1, 2005

### Natasha1

As I don't know how to use this latex coding here it goes....

if I represent by E the sum of terms where k=1 and n is the unknown

I need to use the formulae for Ek and Ek^2 to obtain a formula for Ek(k+1), by simplifying the algebra as much as possible.

Can someone help with this please?

2. Nov 1, 2005

### amcavoy

$$\sum_{k=1}^nk\left(k+1\right)$$

?

If so, note that k(k+1)=k2+k.

3. Nov 1, 2005

### Natasha1

Yes I am asking exactly that :-).

Could someone start this problem, because I am stuck? Thank you :shy:

4. Nov 1, 2005

### pinodk

You have seen the last line of the above reply right?
So you have:
$$\sum_{k=1}^nk\left(k+1\right)=\sum_{k=1}^n k^2+\sum_{k=1}^nk$$
that should take you off

5. Nov 1, 2005

### Natasha1

Ok so now I get

= 1^2+1+2^2+2+3^3+3+.....+n^2+n

and then what do I do?

= n^2 + n

Last edited: Nov 1, 2005
6. Nov 2, 2005

### pinodk

If I understand your assignment correctly, you already have the formulas for the two expressions

$$\sum_{k=1}^n k^2$$
$$\sum_{k=1}^nk$$

So just put a "+" between them :-) and simplify them even more if possible...

But being foreign and all, i could have misinterpreted what you wrote, so please dont hate me if thats the case ;-)

7. Nov 2, 2005