求lim(n→∞)∑(i=1到n)[e^((1⼀n)sin(i⼀n))-1]

2025-02-26 06:28:43
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回答1:

对e^((1/n)sin(i/n))-1用一阶泰勒展开,余项在n取极限时化为0,剩下lim(n→∞)∑(i=1到n)(1/n)sin(i/n),用积分定义,最后得1- cos1