Let `C_n` be a circle of radius `(2/3)^n` centered at the origin for `n = 0, 1, 2,....... and A_n` be the area of the region that is inside the circle `C_(2n)` and outside the circle `C_(2n+1)` for `n = 0, 1, 2,......`.The value of the `sum_(n=0)^oo A_n` equals

8. Let S, be a square of unit area. A circle C_1, is inscribed in S_1, a square S_2, is inscribed in C_1 and so on. In general, a circle C_n is inscribed in the square S_n, and then a square S_(n+1 is inscribed in the circle C_n. Let a_n denote the sum of the areas of the circle C_1,C_2,C_3,.....,C_n then lim_(n->oo) a_n must be

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.

The sum of sum_(n=1)^(oo) ""^(n)C_(2) . (3^(n-2))/(n!) equal

The sum of sum_(n=1)^(oo) ""^(n)C_(2) . (3^(n-2))/(n!) equal

If C_(1),C_(2),C_(3),... is a sequence of circles such that C_(n+1) is the director circle of C_(n) . If the radius of C_(1) is 'a', then the area bounded by the circles C_(n) and C_(n+1) , is

If C_(1),C_(2),C_(3),... is a sequence of circles such that C_(n+1) is the director circle of C_(n) . If the radius of C_(1) is 'a', then the area bounded by the circles C_(n) and C_(n+1) , is

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

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

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)