Prove that 2n > n ∀positive integers n.
Uploaded bysandeep View Answer
Prove 11n+2 + 122n+1 is divisible by 133.
Prove that 12n + 25n-1 is divisible by 13
The sum of the cubes of three consecutive natural no. is divisible by 9.
Prove (x2n-1) is divisible by (x-1).
Prove that 32n+2 – 8n – 9 is divisible by 8
Show that the sum of the first n odd natural no is n2..
Show that 23n – 1 is divisible by 7
Prove that n (n + 1) (2n + 1) is divisible by 6.
Prove that x2n – y2n is divisible by x + y.
Prove by PMI (ab)n = an bn
Using induction, prove that 10n + 3.4n+2 + 5 is divisible by 9 ∀ n∈N
Prove that 41n – 14n is a multiple of 27
Prove that 2.7n + 3.5n – 5 is divisible by 24 ∀ n ∈ N
Prove 1.2+2.22+3.23+…+n.2n = (n-1)2 n + 1+2
Prove (2n+7)<(n+3)2
Prove that 102n-1 +1 is divisible by 11
Prove that n(n +1)(n + 5) is multiple of 3.
For every integer n, prove that 7n - 3nis divisible by 4.
Prove the following by using the principle of mathematical induction for all
(2n +7) < (n + 3)2
Prove the following by using the principle of mathematical induction for all n ∈ N: 41n - 14n is a multiple of 27.
Prove the following by using the principle of mathematical induction for all n ∈ N: 32n + 2 - 8n - 9 is divisible by 8.
Prove the following by using the principle of mathematical induction for all n ∈ N: x2n - y2n is divisible by x+ y.
Prove the following by using the principle of mathematical induction for all n ∈ N: 102n - 1 + 1 is divisible by 11.
Prove the following by using the principle of mathematical induction for all n ∈ N: n (n + 1) (n + 5) is a multiple of 3.
Prove the following by using the principle of mathematical induction for all n ∈ N:
Prove the following by using the principle of mathematical induction for all n ∈ N: 1.2 + 2.22 + 3.22 + … + n.2n= (n - 1) 2n+1 + 2
Prove the following by using the principle of mathematical induction for all n ∈ N: 1.2.3 + 2.3.4 + … + n(n + 1) (n + 2) =