If `A_(n)` is the area bounded by y=x and `y=x^(n), n in N,` then `A_(2).A_(3)…A_(n)=`

If A_(n) is the area bounded by y=(1-x^(2))^(n) and coordinate axes,n in N, then

( 1 + x + x^(2))^(n) = a_(0) + a_(1) x + a_(2) x^(2) + …+ a_(2n) x^(2n) , then a_(0) + a_(1) + a_(2) + a_(3) - a_(4) + … a_(2n) = .

If a_(1), a_(2), a_(3), ……. , a_(n) are in A.P. and a_(1) = 0 , then the value of (a_(3)/a_(2) + a_(4)/a_(3) + .... + a_(n)/a_(n - 1)) - a_(2)(1/a_(2) + 1/a_(3) + .... + 1/a_(n - 2)) is equal to

If f(x+y)=f(x)f(y) for all x and y,f(1)=2 and a_(n)=f(n),n in N, then the equation of the circle having (a_(1),a_(2)) and (a_(3),a_(4)) as the ends of its one diameter

If a_(1), a_(2), a_(3),….,a_(n) are in AP and a_(1) = 0 , then the value of ((a_(3))/(a_(2)) + (a_(4))/(a_(3)) +...+(a_(n))/a_(n-1))-a_(2) ((1)/(a_(2)) + (1)/(a_(3))+...+(1)/(a_(n-2))) is equal to a) (n-2) + (1)/((n-2)) b) (1)/((n-2)) c)(n - 2) d)(n - 1)

If a_(1),a_(2)...a_(n) are the first n terms of an Ap with a_(1)=0 and d!=0 then (a_(3)-a_(2))/(a_(2))+(a_(4)-a_(2))/(a_(3))+(a_(5)-a_(2))/(a_(4))...+(a_(n)-a_(2))/(a_(n-1)) is

If a_(1),a_(2),a_(3)….a_(n) are positive and (n-1)s = a_(1)+a_(2)+….+ a_(n) then prove that a_(1),a_(2),a_(3)…a_(n) ge (n-1)^(n)(s-a_(1))(s-a_(2))….(s-a_(n))