Consider the product series:
$(x-a)$ $(x^{2} -b)$ .......$(x^{14} -n)$
I want to express the result in this form:
$x^{1+2+3+.....14}$ + (some constant)$x^{1+2+3+...14-1}$ +.......so on
My question is how to find the general expression for the coefficients for every powers of x(which are decreasing)?
I have no idea please help me
Is there any formula which can help me?
No, there isn't a general formula. You know that the leading term is $x^105$ because $\sum_{k=1}^{14}{k}=105.$ Now the next term must be $-ax^{104}$ because there's only one way to get $x^{104}.$ Similarly, the third term is $-bx^{103}.$ But when we get to $x^{102}$ things change. We might have multiplied all the variables but $x^3$ or all the variables but $x$ and $x^2$, so the coefficient is $ab-c$. Things will get more complicated as you go along. There are $2^{14}=16,384$ ways to pick which constants to multiply together, and only 106 terms among which to distribute the products, so it's going to get messy.
May I ask why you want to know the individual terms? It seems like you've got a pretty simple formula now.