limn(sin1/n+sin2/n+...+sin100/n)求极限过程lim n→∞ n(sin1/n+sin2/n+...+sin100/n)=?

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limn(sin1/n+sin2/n+...+sin100/n)求极限过程limn→∞n(sin1/n+sin2/n+...+sin100/n)=?limn(sin1/n+sin2/n+...+sin

limn(sin1/n+sin2/n+...+sin100/n)求极限过程lim n→∞ n(sin1/n+sin2/n+...+sin100/n)=?
limn(sin1/n+sin2/n+...+sin100/n)求极限过程
lim n→∞ n(sin1/n+sin2/n+...+sin100/n)=?

limn(sin1/n+sin2/n+...+sin100/n)求极限过程lim n→∞ n(sin1/n+sin2/n+...+sin100/n)=?
原式= lim (sin1/n + sin2/n+...+sin100/n)/(1/n)
=lim (sin1/n)/(1/n) + lim (sin (2/n))/(1/n) + ... lim sin(100/n)/(1/n)
=lim (1/n)/(1/n) + lim (2/n)/(1/n)+...+ lim (100/n)/(1/n)
=1+2+...+100
=5050

lim n→∞ n(sin1/n+sin2/n+...+sin100/n)=?
n=1/t n→∞ t→0 2t→0 … 100t→0
= lim t→0 sin(t)/t+2sin(2t)/(2t)+...+100sin(100t)/(100t)
=1+2+3+4+…+100=5050