>>848
A[n] = (1/n){√(4-(1/n)^2) + √(4-(2/n)^2) + √(4-(3/n)^2) + … + √(4-(2-(1/n))^2)}
f(x) = √(4-x^2) とすると
A[n] = (1/n){f(1/n) + f(2/n) + f(3/n) + … + f(2-(1/n))}

∴ lim[n→∞]A[n] = ∫[0,2]f(x)dx
= ∫[0,2] √(4-x^2) dx = π