Principle of Ma...

If $$n(n^{2}-1)$$ is divisible by $$24$$, then which of the following statements is true?

If $$\forall m\in N$$, then $$11^{m+ 2}+12^{2m-1}$$ is divisible by

If $$n$$ is an even number, then the digit in the units place of $$2^{2n}+1$$ will be 

Let $$P(n):1+\displaystyle \frac{1}{4}+\frac{1}{9}+\ldots..+\frac{1}{n^{2}}<2-\frac{1}{n}$$ is true for

Let $$x > -1$$, then statement $$p(n):(1 + x)^{n} > 1 + nx$$, where  $$ n \in N$$ is true for

$$n(n+1) (n+5)$$ is a multiple of $$3$$ is true for

$$1.2 +2.2^2 +3.2^3+ .................+ n.2^n = (n-1)2^{n+1} + 2$$ is true for

If $$n\in N$$, then $$n(n^2-1)$$ is divisible by

Using mathematical induction,
$$\displaystyle \left ( 1 - \frac{1}{2^2} \right ) \left ( 1 - \frac{1}{3^2} \right ) \left ( 1 - \frac{1}{4^2} \right ) ......... \left ( 1 - \frac{1}{(n + 1)^2} \right )$$

For all positive integers $$n$$, $$P(n)$$ is true , and $$2^{n-2}>3n$$, then which of the following is true?