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

[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?

 

[amcavoy]

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?

Are you asking for:

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

?

If so, note that k(k+1)=k²+k.

 

[Natasha1]

Are you asking for:
$$\sum_{k=1}^nk\left(k+1\right)$$
?
If so, note that k(k+1)=k²+k.

Yes I am asking exactly that :-).

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

 

[pinodk]

Are you asking for:
$$\sum_{k=1}^nk\left(k+1\right)$$
?
If so, note that k(k+1)=k²+k.

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

 

[Natasha1]

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

Ok so now I get

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

and then what do I do?


Is the answer then

= n^2 + n

 

[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 don't hate me if that's the case ;-)

 

[benorin]

Here you go Natasha, (link)

Yes I am asking exactly that :-).
Could someone start this problem, because I am stuck? Thank you :shy:

Here is a link to the answer I posted on your other thread:

https://www.physicsforums.com/showthread.php?t=97842