If `n>3` and `a,b in R` ,then the value of `ab-n(a-1)(b-1)+(n(n-1))/(1.2)(a-2)(b-2)-.....+(-1)^(n)(a-n)(b-n)` is equal to

If a>b and n is a positive integer,then prove that a^(n)-b^(n)>n(ab)^((n-1)/2)(a-b)

If tan x=n tan y,n in R^(+), then the maximum value of sec^(2)(x-y) is equal to (a) ((n+1)^(2))/(2n) (b) ((n+1)^(2))/(n)( c) ((n+1)^(2))/(2) (d) ((n+1)^(2))/(4n)

Determinant |{:(a+b+nc,(n-1)a,(n-1)b),((n-1)c,b+c+na,(n-1)b),((n-1)c,(n-1)a,c+a+nb):}| is equal to

The arithmetic mean of 1,2,3,...n is (a) (n+1)/(2) (b) (n-1)/(2) (c) (n)/(2)(d)(n)/(2)+1

The value of sum_(r=1)^(n)(-1)^(r+1)(^nCr)/(r+1) is equal to a.-(1)/(n+1) b.(1)/(n) c.(1)/(n+1) d.(n)/(n+1)

If a>b>0, with the aid of Lagranges mean value theorem,prove that nb^(n-1)(a-b) 1nb^(n-1)(a-b)>a^(n)-b^(n)>na^(n-1)(a-b),quad if 0

If b_(1),b_(2),b_(3),"….."b_(n) are positive then the least value of (b_(1) + b_(2) +b _(3) + "….." + b_(n)) ((1)/(b_(1)) + (1)/(b_(2)) + "….." +(1)/(b_(n))) is