If there is a positive integer n such that (n+1)! + (n+2)! = n! 440, then the sum of the digits of n is

If n is a positive integer, then ((n+4)!)/((n+7)!)=

If N denotes the set of all positive integers and if f : N -> N is defined by f(n)= the sum of positive divisors of n then f(2^k*3) , where k is a positive integer is

If n is a positive integer, then show tha 3^(2n+1)+2^(n+2) is divisible by 7 .

The least positive integer n such that ((2i)/(1+i))^(n) is a positive integer is

If n is a positive integer then int_(0)^(1)(ln x)^(n)dx is :

If n is a positive integer then 2^(4n) - 15n - 1 is divisible by

If n is an odd positive integer, show that (n^2-1) is divisible by 8.

If n is an odd positive integer, show that (n^2-1) is divisible by 8.

If the average of n consecutive integers equal to 1? (1) n is even. (2) If S is the sum of the n consecutive integers, then 0ltSltn

If n ge 1 is a positive integer, then prove that 3^(n) ge 2^(n) + n . 6^((n - 1)/(2))