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

问题描述:

求lim(n→∞)∑(i=1到n)[e^((1/n)sin(i/n))-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