If A = 1201, then by the principle of Mathematical induction, prove that An = 12n01
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
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
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