If A = 1201, then by the principle of Mathematical induction, prove that An = 12n01
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
B.
Given, a0 = 1, an + 1 = 3n2 + n + an⇒ a1 = 30 + 0 + a0 = 1and a2 = 312 + 1 + a1 = 3 + 1 + 1 = 5From option (b),Let P(n) = n3 - n2 + 1∴ P(0) = 0 - 0 + 1 = 1 = a0 P(1) = 12 - 12 + 1 = 1 = a1 P(2) = 22 - 22 + 1 = 1 = a2Hence option b is correct