Principle of Ma...

If $$P(n)$$ be the statement $$n(n+1)+1$$ is odd, then which of the following is false?

Let $$P\left ( n \right )=2^{3n}-7n-1$$ then $$P(n)$$ is divisible by

Let $$P(n)$$ be the statement representing the sum of next three successive natural numbers of $$n$$, $$\forall n\in N$$, then the smallest value of $$n$$ to which $$P(n)$$ is divisible by $$9$$ is

Let $$P\left ( k \right ):2+4+6+...+2k=k\left ( k+1 \right )+2$$, then the statement $$P(m+1)$$ will be true if

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

$$P\left ( n \right ):2^{n+2}< 3^{n}$$, is true for

Let $$P(n)$$ be the statement that $$n^{2}-n+41$$ is prime, then which of the following is not true ?

Let $$P\left ( n \right ):2^{n}> n, \forall n\in N$$ and $$2^{k}> k, \forall n=k$$, then which of the following is true $$\forall k\geq 2$$?

The inequality, $$P(n)=n!> 2^{n}$$ is true for

Let $$P\left ( n \right ):a^{n}+b^{n}$$ such that $$a, b$$ are even, then $$p(n)$$ will be divisible by $$a + b$$ if