If `f(n)=|(n!, (n+1)!, (n+2)!),((n+1)!, (n+2)!, (n+3)!), ((n+2)!, (n+3)!, (n+4)!)|` Then the value of 1/1020[(f(100))/(f(99))]` is

If f(x)=|{:(x^(n),sinx,cosx),(n!,"sin"(npi)/(2),"cos"(npi)/(2)),(a,a^(2),a^(3)):}| , then the value of (d^(n))/(dx^(n))(f(x))" at "x=0" for "n=2m+1 is

For a fixed positive integer n , if =|n !(n+1)!(n+2)!(n+1)!(n+2)!(n+3)!(n+2)!(n+3)!(n+4)!| , then show that [/((n !)^3)-4] is divisible by ndot

Let f(x)=(x-1)(x-2)(x-3)(x-n),n in N ,a n df(n)=5040. Then the value of n is________

Let f(x)=(x-1)(x-2)(x-3)(x-n),n in N ,a n df(n)=5040. Then the value of n is________

Let f(x)=(x-1)(x-2)(x-3)--(x-n),n in N ,a n df(n)=5040. Then the value of n is________

For x in R , x ne0, 1, let f_(0)(x)=(1)/(1-x) and f_(n+1)(x)=f_(0)(f_(n)(x)),n=0,1,2….. Then the value of f_(100)(3)+f_(1)((2)/(3))+f_(2)((3)/(2)) is equal to

f(1)=1, n ge 1 f(n+1)=2f(n)+1 then f(n)=

Let Delta_(a)=|{:((a-1),n,6),((a-1)^(2), 2n^(2),4n-2),((a-1)^(3),3n^(3),3n^(2)-3n):}| the value of sum_(a=1)^(n)Delta_(a) is

Let f(x)=lim_(nto oo) 1/n((x+1/n)^(2)+(x+2/n)^(2)+……….+(x+(n-1)/n)^(2)) Then the minimum value of f(x) is

If f (n)= 1/pi int _(0) ^(pi//2) (sin ^(2) (n theta) d theta)/(sin ^(2) theta), n in N, then evulate (f (15)+ f (3))/( f (12) -f (10)).