How to calculate this product

[desperate]

hi !

I have some trouble calculating this product:

S=(1-x^k) * (1-(x+1)^k) * (1-(x+2))^k * (1-(x+3))^k .... (1-(x+n))^k

I know that ln(1-x) = x (approximatively)

When applying the logarithm I get

ln(S)= x^k + (x+1)^k + (x+2)^k + ... + (x+n)^k

So:

S= exp (x^k + (x+1)^k + (x+2)^k + ... + (x+n)^k)

I want to bound this but I don't know how to do it from here.

Thank you !

[imatfaal]

are you sure of your brackets - the progression seems to change from necessary bracket to superfluous. we do have latex tags btw if that helps. do you have any limits to x, k, &n?

[mathematic]

ln(1+x) = x - x^2/2 + ..... ln(1-x) starts with -x.

[desperate]

yes I'm sorry, I made a mistake with the brackets:

 

The exact expression is: S=(1-x^k) * (1-(x+1)^k) * (1-(x+2)^k) * (1-(x+3)^k) .... (1-(x+n)^k)