1/3*5+1/5*7+······+1/97*99+1/99*101=?
问题描述：
1/3*5+1/5*7+······+1/97*99+1/99*101=?
答
1/1*3+1/3*5+1/5*7+.+1/99*100-1/1*3 =1/2[( 1-1/3)+(1/3-1/5)+(1/5-1/7)+.+(1/99-1/100)]-1/1*3 =1/2( 1-1/3+1/3-1/5+1/5-1/7+.+1/99-1/100)-1/1*3 =1/2(1-1/100)1-1/1*3 =99/200-1/1*3 =74/150