Question 0509

Show that where ${A}$ and ${B}$ are constants to be found.

Hence find ${\displaystyle \sum_{r=5}^n \frac{5 n - 1}{r^3-r}.}$
(There is no need to express your answer as a single algebraic fraction.)

Give a reason why the series ${\displaystyle \sum_{r=5}^\infty \frac{5 n - 1}{r^3-r}}$ converges, and write down its value.