1，∑1/(n+i)
=1/n*∑1/(1+i/n)
=∫(0->1)1/(1+x)dx=ln2
2，∑1/(2in-i^2)^1/2
=1/n*∑1/(2i/n-i^2/n^2)^1/2
=∫(0->1)1/(2x-x^2)^1/2dx
=∫(0->1)1/[1-(1-x)^2]dx
令1-x=sint有
原式=-∫costdt/cost=-arcsin(1-x)
=π/2
3，sin(π/n)∑cos^2πi/n
=sin(π/n)/(1/n)*(1/n)∑cos^2πi/n
=(π/n)∑cos^2πi/n
=∫(0->π)cos^2xdx
=π/2