雄县顺丰快递电话:1/4+1/12+1/24+1/40+……+1/19800=?

来源:百度文库 编辑:杭州交通信息网 时间:2024/05/06 12:10:48

解:1/4+1/12+1/24+1/40+……+1/19800
=(1/2)*[1/2+1/6+1/12+1/20+...+1/9900]
=(1/2)*[1/1*2+1/2*3+1/3*4+1/4*5+...+1/99*100]
=(1/2)*[1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/99-1/100]
=(1/2)*[1-1/100]
=(1/2)*(99/100)
=99/200

原式=1/4*[1/1+1/(1+2)+1/(1+2+3)……+1/(1+2+3+……+99)]