2025 RVHS Promo Q6

2025 RVHS Promo Q6

Junior College 1
7 marks
  1. A sequence is such that \(u_{n+1}=ku_n+5\), for \(n\geq 1\) where \(k\) is a constant and \(u_1=3\).
    Describe the behaviour of the sequence when
    1. \(k=2\),[1]
    2. \(k=-\dfrac{2}{3}\).[1]
  2. It is known that \(\displaystyle \sum_{r=1}^{n}\frac{1}{(r+1)(r-1)!}=1-\frac{1}{(n+1)!}\).
    1. Explain why \(\displaystyle \sum_{r=1}^{\infty}\frac{1}{(r+1)(r-1)!}\) converges and state the value it converges to.[2]
    2. Find \(\displaystyle \sum_{r=6}^{N}\frac{1}{r(r-2)!}\) in terms of \(N\).[3]

Solution:

Solution locked

Sign in to view the step-by-step solution

Similar questions are unavailable for this question.
Answer:Converges to \(1\); \(\sum_{r=6}^{N}\dfrac1{r(r-2)!}=\dfrac1{120}-\dfrac1{N!}\)

Need help? Join our JC Math tuition classes.

Learn more