If `sum_(n=1)^n u_n =an^2+bn+c, then |(u_1,u_2,u_3),(1,1,1),(7,8,9)|=`
(A) 0 (B) `u_1-u_2+u_3` (C) 1 (D) none of these

The circles x^2 + y^2 + 2ux + 2vy = 0 and x^2 + y^2 + 2u_1 x + 2v_1 y = 0 touch each other at (1, 1) if : (A) u + u_1 = v + v_1 (B) u + v = v_1 + u_1 (C) u/u_1 = v/v_1 (D) none of these

The value of sum_(n=1)^(N) U_n=|{:(n,1,5),(n^2,2N+1,2N+1),(n^3,3N^2,3N):}| is

Let A=((1,0,0),(2,1,0),(3,2,1)) . If u_(1) and u_(2) are column matrices such that Au_(1)=((1),(0),(0)) and Au_(2)=((0),(1),(0)) , then u_(1)+u_(2) is equal to :

If u_n=sin^("n")theta+cos^ntheta, then prove that (u_5-u_7)/(u_3-u_5)=(u_3)/(u_1) .

If u_n=sin^("n")theta+cos^ntheta, then prove that (u_5-u_7)/(u_3-u_5)=(u_3)/(u_1) .

If U={:[(1,2,2),(-2,-1,-1),(1,-4,-3)]:}' ,sum of elements of inverse of U is

("lim")_(xvecoo){1/(1-n^2)+2/(1-n^2)+......n/(1-n^2)}i se q u a lto 0 (b) -1/2 (c) 1/2 (d) none of these

Given that u_(n+1)=3u_n-2u_(n-1), and u_0=2 ,u_(1)=3 , then prove that u_n=2^(n)+1 for all positive integer of n

If u_(n) = int_(0)^(pi/2) x^(n)sinxdx , then the value of u_(10) + 90 u_(8) is : (a) 9(pi/2)^(8) (b) (pi/2)^(9) (c) 10 (pi/2)^(9) (d) 9 (pi/2)^(9)

Let u_(1)=1,u_2=2,u_(3)=(7)/(2)and u_(n+3)=3u_(n+2)-((3)/(2))u_(n+1)-u_(n) . Use the principle of mathematical induction to show that u_(n)=(1)/(3)[2^(n)+((1+sqrt(3))/(2))^n+((1-sqrt(3))/(2))^n]forall n ge 1 .