If A = 1201, then by the principle of Mathematical induction

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11.

If A = 1201, then by the principle of Mathematical induction, prove that An12n01


Since, A = 1201Let Pn : An = 12n01         ...(i)P1 : A = 12 . 101 = 1201  P(n) is true for n = 1.Let P(n) is true for n = k.                    Pk : Ak = 12k01                ...(ii)Now, Pk + 1 : Ak + 1 = 12k + 101      ...(iii)    Ak + 1 = Ak × A1 = 12k011201                                   = 12k + 101 P(n) is true for n = k + 1.Hence, P(n) is true for all n  N


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 Multiple Choice QuestionsMultiple Choice Questions

12.

The value of 2, 6, 10 ... (4n - 6)(4n - 2) is equal to

  • C(2n, n)

  • (n + 1)(n + 2)(n + 3) ... (2n)

  • n! P (2n, n)

  • None of above


13.

Using mathematical induction, the numbers an 's are defined by,a0 = 1, an + 1 = 3n2 + n + an, n  0Then an = ?

  • n3 + n2 + 1

  • n3 - n2 + 1

  • n3 - n2

  • n3 + n2


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