If `P=n(n^2-1^2)(n^2-2^2)(n^2-3^2)........(n^2-r^2), n > r , n in N` then P is divisibe by

P(n) : 1^(2) + 2^(2) + 3^(2) + .......+ n^(2) = n/6(n+1) (2n+1) n in N is true then 1^(2) +2^(2) +3^(2) + ........ + 10^(2) = .......

If A={p:p=((n+2)(2n^(5)+3n^(4)+4n^(3)+5n^(2)+6))/(n^(2)+2n), n p in Z^(+)} then the number of elements in the set A, is

If A={p:p=((n+2)(2n^(5)+3n^(4)+4n^(3)+5n^(2)+6))/(n^(2)+2n), n p in Z^(+)} then the number of elements in the set A, is

If for any +ve integer n Delta_(n)=[[2r-1,^(n)C_(r),1n^(2)-1,2^(n),n+1cos^(2)(n^(2)),cos^(2)(n),cos^(2)(n+1)] then sum_(r=0)^(n)Delta_(r),n in N, is equal to

If P(n) :1+4+7…….+(3n-2)=(1)/(2)n(3n-1) .Verify P(n) for n =1,2.

If S_(n)=sum_(r=1)^(n)(1+2+2^(2)+......+2^(r))/(2^(r)), then S_(n) is equal to (a)2^(n)n-1( b) 1-(1)/(2^(n))(c)2n-1+(1)/(2^(n))(d)2^(n)-1

If "^(2n+1)P_(n-1):^(2n-1)P_n=3:5, then find the value of n .

If "^(2n+1)P_(n-1):^(2n-1)P_n=3:5, then find the value of n .