I need to use algebraic manipulation to rewrite the sum:
$$\sum_{k=1}^N\frac{1}{\sqrt {(k^3-x)}}-\frac{1}{\sqrt {(k^3+x)}}$$
I think I'm supposed to write it using matrices $Ax = b$ for linear algebra but I'm not sure I'm on the right path. Is that the right path? How do I write $\frac{1}{\sqrt {(k^3-x)}}$ as a matrix?
In this exercise, as we can guess, there are expected algebraic manipulations to obtain a form more convenient for computations. For example: $$ \sum_{k=1}^N\frac{1}{\sqrt {(k^3-x)}}-\frac{1}{\sqrt {(k^3+x)}} =\sum_{k=1}^N\frac{\sqrt {(k^3-x)}+\sqrt {(k^3+x)}}{\sqrt{k^6-x^2}}. $$ But all depends on a goal of such algebraic manipulations.