1/4+1/12+1/24+1/40……+1/19800=?
问题描述：
1/4+1/12+1/24+1/40……+1/19800=?
答
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
答
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)*(99/10...