सिद्ध कीजिए की : `n(n+1)(2n+1), AA n in N` के लिए 6 से विभाजित है।

Prove 1 + 5 + 9 + ... + (4n - 3) = n(2n - 1), AA n in N

Show that the function f:N rarr N, given by f(n)=n- (-1)^(n), AA n in N is a bijection.

If A = {0,1} and N be the set of natural numbers. Then , the mapping f: N rarr A defined by f(2n-1) = 0 , f(2n) = 1, AA n in N , is onto.

Given f(1)=2 and f(n+1)=(f(n)-1)/(f(n)+1)AA n in N then

The greatest natural number which divides n(n+1)(2n+1), AA n in N is

The greatest positive integer which divides n (n+1)(n+2)….. (n+r-1), AA n in N is