Mathematics · Mathematical Induction
In the principle of mathematical induction, consider the statement P(n): 11 × 2 × 3 + 12 × 3 × 4 + ... + 1n(n + 1)(n + 2) = n(n + 3)4(n + 1)(n + 2) for all n ∈ N. If P(k) is assumed to be true, then the value of P(k) + 1(k + 1)(k + 2)(k + 3) before simplification is equal to which of the following expressions?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1(k + 1)(k + 3) + 4(k + 1)(k + 2)(k + 3)
- 2k(k + 3)2 + 44(k + 1)(k + 2)(k + 3)✓
- 3(k + 1)(k + 3)4(k + 1)(k + 2)(k + 3)
- 4k(k + 3)4(k + 1)(k + 2)(k + 3)
Correct answer
k(k + 3)2 + 44(k + 1)(k + 2)(k + 3)
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