2026 NASS P1 Q3

2026 NASS P1 Q3

Secondary 4
6 marks
  1. Express \(\dfrac1{n(n+1)}\) in partial fractions.[3]
  2. Hence show that \(\dfrac1{3(4)}+\dfrac1{4(5)}+\dfrac1{5(6)}+\cdots+\dfrac1{(n-1)n}+\dfrac1{n(n+1)}=\dfrac{n-2}{3(n+1)}\).[3]

Solution:

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Answer:(a) \(\dfrac1n-\dfrac1{n+1}\). (b) \(\dfrac{n-2}{3(n+1)}\).

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