Principle of Ma...

Let P(n) be a statement and let P(n) ⇒ P( n + 1 ) for all natural numbers n , then what will the nature of  P(n) ?

Let P(n) b e a statement 2n < n! , where n is a natural number , then P(n)is true for

If x > -1 , then the statement ( 1 + x ) n > 1 + nx is true for

If P ( n ) = 2+4+6+………………..+2n , n ∈ N , then P ( k ) = k ( k + 1 ) + 2 ⇒ P ( k + 1 ) = ( k + 1 ) ( k +2 ) + 2 for all k ∈ N . So we can conclude that P ( n ) = n ( n + 1 ) +2 for

(xⁿ − yⁿ) is divisible by ( x - y ) for 

The greatest positive integer , which divides n ( n + 1 ) ( n + 2 ) ( n + 3 ) for all n ∈ N , is

Let P ( n ) denote the statement n² + n is odd , It is seen that P(n) ⇒ P( n + 1 ) , therefore P ( n ) is true for all

The greatest positive integer, which divides (n + 1) (n + 2) (n + 3)..................(n + r)∀n ∈ W , is