If `A_n` be the area bounded by the curve `y=(tanx^n)` ands the lines `x=0,\ y=0,\ x=pi//4` , then for `x > 2.` `A_n+A_(n-1)=1/(n-1)` b. `A_n+A_(n-2)<1/(n-1)` c. `A_n+A_(n-2)=1/(n-1)` d. none of these

If A_n be the area bounded by the curve y=(tanx^n) ands the lines x=0,\ y=0,\ x=pi//4 Prove that for n > 2. , A_n+A_(n+2)=1/(n+1) and deduce 1/(2n+2)< A_(n) <1/(2n-2)

Let A_(n) be the area bounded by the curve y=x^(n)(n>=1) and the line x=0,y=0 and x=(1)/(2). If sum_(n=1)^(n)(2^(n)A_(n))/(n)=(1)/(3) then find the value of n .

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

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=x and y=x^(n),n in N, then A_(2)*A_(3)...A_(n)=(1)/(n(n+1)) (b) (1)/(2^(n)n(n+1))(1)/(2^(n-1)n(n+1)) (d) (1)/(2^(n-2)n(n+1))

If alpha, beta arethe roots of the equation x^2-ax+b=0 and A_n=alpha^n+beta^n then which of the following is true? (A) A_(n+1)=aA_n+bA_(n-1) (B) A_(n+1)=bA_n+aA_(n-1) (C) A_(n+1)=aA_n-bA_(n-1) (D) A_(n+1)=bA_n+-aA_(n-1)

Let {A_n} be a unique sequence of positive integers satisfying the following properties: A_1 = 1, A_2 = 2, A_4 = 12, and A_(n+1) . A_(n-1) = A_n^2 pm 1 for n = 2,3,4… then , A_7 is

If the sequence {a_n}, satisfies the recurrence, a_(n+1) = 3a_n - 2a_(n-1), n ge2, a_0 = 2, a_1 = 3, then a_2007 is

If A_(1),A_(2),A_(3),…,A_(n) are n points in a plane whose coordinates are (x_(1),y_(1)),(x_(2),y_(2)),(x_(3),y_(3)),…,(x_(n),y_(n)) respectively. A_(1)A_(2) is bisected in the point G_(1) : G_(1)A_(3) is divided at G_(2) in the ratio 1 : 2, G_(3)A_(5) at G_(4) in the1 : 4 and so on untill all the points are exhausted. Show that the coordinates of the final point so obtained are (x_(1)+x_(2)+.....+ x_(n))/(n) and (y_(1)+y_(2)+.....+ y_(n))/(n)