lim n→∞(sin(π/n))∑(1/(1+cos(k/n))) = 其中k=1~n

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limn→∞(sin(π/n))∑(1/(1+cos(k/n)))=其中k=1~nlimn→∞(sin(π/n))∑(1/(1+cos(k/n)))=其中k=1~nlimn→∞(sin(π/n))∑(

lim n→∞(sin(π/n))∑(1/(1+cos(k/n))) = 其中k=1~n
lim n→∞(sin(π/n))∑(1/(1+cos(k/n))) = 其中k=1~n

lim n→∞(sin(π/n))∑(1/(1+cos(k/n))) = 其中k=1~n
lim( n→∞)(sin(π/n))∑(1/(1+cos(k/n)))
= lim (n→∞)(π/n)∑(1/(1+cos(k/n)))
=π∫[0,1]1/(1+cosx)dx
=π∫[0,1](1-cosx)/(1-cos²x)dx
=π∫[0,1](1/sin²x-cosx/sin²x)dx
=π(-cotx+1/sinx)|[0,1]
=π(1-cosx)/sinx|[0,1]
=π[(1-cos1)/sin1-lim(x->0)(1-cosx)/sinx]
=π[(1-cos1)/sin1-1/2]