Mathematical In...

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

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

Which of the following numbers will divide n³ + 3n² + 5n + 3 for all n belonging to natural numbers?

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

(xⁿ−yⁿ)is divisible by ( x - y ) for 

Which of the following will be true for every x ∈ R?

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