Home
Class 12
MATHS
If P=n(n^2-1^2)(n^2-2^2)(n^2-3^2).........

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

A

`(2r+2)!`

B

`(2r-1)!`

C

`(2r+1)!`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B, C
Promotional Banner

Similar Questions

Explore conceptually related problems

If =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 (n^(2)-3^(2))......*(n^(2)-r^(2)),n>r,n in N

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

Show that ""^(n)P_(n)=2""^(n)P_(n-2)

If C_(r) stands for ""^(n)C_(r) , then the sum of the series (2((n)/(2))!((n)/(2))!)/(n!)[C_(0)^(2)-2C_(1)^(2)+3C_(2)^(2)-...+(-1)^(n)(n+1)C_(n)^(2)] , where n is an even positive integers, 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.