What is the sum formula for this expression

[bomba923]

What is the sum formula for this expression??

"The sum from n=1 to k of (n^c) for any real constant c"

k
sigma (n^c)
n=1


(lower limit n=1, upper limit k) for the sum (n^c), where c is any real constant

 

[bomba923]

Sorry, um, the text file needed mathtype to view

Um, here's a GIF gif picture format; i attached it and it will open easily (gif picture format) it's an attachment, the GIF image format formula; it will open easily i hope (whtisthsum.gif)

 

[TenaliRaman]

Well it would be (c+1)th degree equation in k
so u can write it as a_(c+1)1*k^(c+1)+a_ck^c+...+a_0

I am not sure whether there is a neat closed form expression which will give u the a_i's ...

-- AI

 

[Zurtex]

http://mathworld.wolfram.com/GeneratingFunction.html

Hope that helps , looks like it is:

\frac{x}{1 - x}

 

[bomba923]

http://mathworld.wolfram.com/GeneratingFunction.html

Hope that helps , looks like it is:

\frac{x}{1 - x}

Yeah, but the n changes, whereas the 'c' stays constant...
it's not to the power of 1, then 2, then 3...but always to an unchanging constant c...only the 'n' changes as u add...

1+(2^c)+(3^c)+(4^c)+(5^c)+(6^c)+...+(k^c)...so the c can be any real value...but c remains constant! only the 'n' changes!<=as u add

That's why this is not really a power series,; the 'c' must be constant, and cannot change! (that's why the \frac{x}{1 - x} doesn't work)!