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If P(n) = 2 + 4 + 6 + ........ + 2n, n ∈ N, then P(k) = k(k + 1) + 2 ⇒ P(k + 1) = (k + 1)(k + 2) + 2 for all k ∈ N. So, we can conclude that P(n) = n(n + 1) + 2 for
  • a)
    all n ∈ N
  • b)
    n > 1
  • c)
    n > 2
  • d)
    Cannot be determined
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
If P(n) = 2 + 4 + 6 + ........ + 2n, n ∈ N, then P(k) = k(k + 1) ...
The rth term of the series is given by:

Putting r = 1, 2,...., n-1, we get

Adding the above equations ,we get 
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If P(n) = 2 + 4 + 6 + ........ + 2n, n ∈ N, then P(k) = k(k + 1) + 2 ⇒ P(k + 1) = (k + 1)(k + 2) + 2 for all k ∈ N. So, we can conclude that P(n) = n(n + 1) + 2 fora)all n ∈ Nb)n > 1c)n > 2d)Cannot be determinedCorrect answer is option 'D'. Can you explain this answer?
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