Principle of Ma...

If x > 1, then the statement $$P(n) : (1 + x)^n > 1 + nx$$ is true for

A student was asked to prove a statement by induction.
(i) $$P(5)$$ is true and
(ii) Truth of $$P(n) \Rightarrow$$ truth of $$P(n + 1)$$, $$n\epsilon N$$
On the basis of this, he could conclude that $$P(n)$$ is true for

If n is a natural number then $$\left (\frac {n+1}{2}\right )^n \geq n!$$ is true when

If $$n \in N$$, then $$x^{2n+1} + y^{2n+1}$$ is divisible by

The inequality $$n! > 2^{n-1}$$ is true

For positive integer n, $$10^{n-2} > 81n$$ when

State which of the following statements is true $$ \displaystyle 2^{16}-1 $$   is divisible by 

Let $$S(K) =1+ 3 + 5...+ (2K -1) =3 + K^2$$. Then which of the following is true

The statement P(n) $$"1 \times 1! + 2\times 2! + 3\times 3! + ... + n \times n! =(n + 1)! 1"$$ is

If $$a, b$$ and $$n$$ are natural numbers then $$a^{2n-1}+b^{2n-1}$$ is divisible by