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 be the area bounded by the curve y=(tanx)^n and the lines x=0,\ y=0,\ x=pi//4 , then for n > 2.

If A_n be the area bounded by the curve y=(tanx)^n and the lines x=0,\ y=0,\ x=pi//4 , then for n > 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)

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)

Let A_(n) between area bounded by the curve y=(tan x)^(n),n in N and the lines y = 0 and x=(pi)/(4) . For n gt 2 , prove that A_(n)+A_(n-2)=(1)/(n-1) and decuce that (1)/(2n+2)lt A_(n)lt (1)/(2n-2)

If the arithmetic mean of x and y is (x^n+y^n)/((x^(n-1)+y^(n-1))) ,then the value of n is

Let a_n=1000^n/(n!) for n in N , then a_n is greatest, when value of n is

If a_n = 2^(2^n) + 1 , then for n>1 last digit of an is