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2025 HCI P1 Q7

2025 HCI P1 Q7

7 marks
  1. Use the formula listed in the List of Formulae (MF27) to explain why\(\sum_{r=0}^{\infty} \frac{1}{r!} = e\)[1]
  2. Show that \(\sum_{r=0}^{\infty} \frac{r+1}{r!} = 2e\).[3]
  3. Find the value, in terms of \(e\), of \(\sum_{r=6}^{\infty} \frac{r+1}{r!}\).[3]

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Answer:(a) \(e\) (b) \(2e\) (c) \(2e-\dfrac{217}{40}\)

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