一道数学题~~呵呵~简便算~在线等~~~~~~!!!!!!!!!!!!!!!!!!!!
1/4+1/12+1/24+1/40+……+1/19800
怎么算啊?我笨不会~请个位大虾帮帮忙~~~~谢谢~再现=
参考答案: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