N2021 P1 Q5

N2021 P1 Q5

Junior College 2
7 marks
  1. Express \(\dfrac{x}{(x+2)(x+3)(x+4)}\) in partial fractions.[3]
  2. Hence find, in terms of \(n\), \(\displaystyle\sum_{r=1}^{n}\dfrac{r}{(r+2)(r+3)(r+4)}\).[3]
  3. State the value of \(\displaystyle\sum_{r=1}^{\infty}\dfrac{r}{(r+2)(r+3)(r+4)}\).[1]

Solution:

Solution locked

Sign in to view the step-by-step solution

Finding similar questions...
Answer:(a) \(-\frac1{x+2}+\frac3{x+3}-\frac2{x+4}\); (b) \(\frac16-\frac{n+2}{(n+3)(n+4)}\); (c) \(\frac16\).

Need help? Join our JC Math tuition classes.

Learn more