Higher Mathematics · Free original practice · 3 marks
Paper preview: a limit with a reason
Work through one question, use a small hint if needed, then compare your reasoning. Suggested marks are for self-assessment; independent subject review is pending.
A sequence has and = 5. Explain why a limit exists and find its exact value.
A small hint
Compare the multiplier with both −1 and 1.
Worked explanation and suggested marking
The multiplier lies strictly between −1 and 1, so the recurrence converges.
Up to 1 mark
At the limit, L = 0.6L + 8, giving 0.4L = 8.
Up to 1 mark
Hence L = 20.
Up to 1 mark
Since −1 < 0.6 < 1, a limit exists. L = 0.6L + 8 gives L = 20.
What to watch for
- A few terms getting closer does not replace the convergence condition.