Question

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

Answer 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