`A_1,A_(2) ....A_(n)` are points on the line y=x lying in the positive quadrant such that `OA_(n)=nOA_(n-1)` .O being the origin.If `OA_(1)=1` and the coordinates of `A_n `,are `(2520sqrt(2),2520sqrt(2))` ,then n=

If A_(1),A_(2)......A_(n) are points on the line y=x lying in the positive quadrant such that OA_(n)=n.OA_(n-1),O being the origin.If OA_(1)=1 then the co-ordinates of A_(8) are (3a sqrt(2),3a sqrt(2),) where a is equal to

A_(1),A_(2),...,A_(n) are the vertices of a regular plane polygon with n sides and O as its centre. Show that sum_(i=1)^(n)vec OA_(i)xxvec OA_(i+1)=(1-n)(vec OA_(2)xxvec OA_(1))

Let A (a,b) be a fixed point and O be the origin of coordionates. If A_(1) is the mid-point of OA, A_(2) is the mid- poind of A A_(1),A_(3) is the mid-point of A A_(2) and so on. Then the coordinates of A_(n) are

If 1, a_1,a_2,a_3 ,…, a_(n-1) are the nth roots of unity then prove that : (1-a_1)(1-a_2)(1-a_3)...(1-a_(n-1)) =n.

If O is the origin anf A_(n) is the point with coordinates (n,n+1) then (OA_(1))^(2)+(OA_(2))^(2)+…..+(OA_(7))^(2) is equal to

If a_(1),a_(2)......a_(n) are n positive real numbers such that a_(1).......a_(n)=1. show that (1+a_(1))(1+a_(2))......(1+a_(n))>=2^(n)

If a_1=1\ a n d\ a_(n+1)=(4+3a_n)/(3+2a_n),\ ngeq1\ a n d\ if\ (lim)_(n->oo)a_n=n then the value of a_n is sqrt(2) b. -sqrt(2) c. 2\ d. none of these

A_1 A_2 A_3............A_n is a polygon whose all sides are not equal, and angles too are not all equal. theta_1 is theangle between bar(A_i A_j +1) and bar(A_(i+1) A_(i +2)),1 leq i leq n-2.theta_(n-1) is the angle between bar(A_(n-1) A_n) and bar(A_n A_1), while theta_n, is the angle between bar(A_n A_1) and bar(A_1 A_2) then cos(sum_(i=1)^n theta_i) is equal to-