1又2/3+2又2/15+3又2/35+.+11又2/483+12又2/575
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/19 00:42:10
![1又2/3+2又2/15+3又2/35+.+11又2/483+12又2/575](/uploads/image/z/4096220-68-0.jpg?t=1%E5%8F%882%2F3%2B2%E5%8F%882%2F15%2B3%E5%8F%882%2F35%2B.%2B11%E5%8F%882%2F483%2B12%E5%8F%882%2F575)
1又2/3+2又2/15+3又2/35+.+11又2/483+12又2/575
1又2/3+2又2/15+3又2/35+.+11又2/483+12又2/575
1又2/3+2又2/15+3又2/35+.+11又2/483+12又2/575
原式=1+2+3+...+11+12+2/3+2/15+2/35+...+2/483+2/575
=(1+12)*12/2+2*(1/3+1/15+1/35+...+1/483+1/575)
=78+2*[1/(1*3)+1/(3*5)+1/(5*7)+...1/(21*23)+1/(23*25)]
=78+2*1/2*(1/1-1/3+1/3-1/5+1/5-1/7+...+1/21-1/23+1/23-1/25)
=78+(1-1/25)
=78+24/25
=78又24/25