1/2*1+1/3*2+1/4*3.+1/2009*2008=就是1/2+1/6+1/12+1/20+.+1/2009*2008
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/06 18:54:26
![1/2*1+1/3*2+1/4*3.+1/2009*2008=就是1/2+1/6+1/12+1/20+.+1/2009*2008](/uploads/image/z/1675044-36-4.jpg?t=1%2F2%2A1%2B1%2F3%2A2%2B1%2F4%2A3.%2B1%2F2009%2A2008%3D%E5%B0%B1%E6%98%AF1%2F2%2B1%2F6%2B1%2F12%2B1%2F20%2B.%2B1%2F2009%2A2008)
1/2*1+1/3*2+1/4*3.+1/2009*2008=就是1/2+1/6+1/12+1/20+.+1/2009*2008
1/2*1+1/3*2+1/4*3.+1/2009*2008=
就是1/2+1/6+1/12+1/20+.+1/2009*2008
1/2*1+1/3*2+1/4*3.+1/2009*2008=就是1/2+1/6+1/12+1/20+.+1/2009*2008
公式:1/n*(n-1)=1/(n-1)-1/n
1/2*1+1/3*2+1/4*3+.+1/2009*2008
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+.+(1/2008-1/2009)
=1-1/2+1/2-1/3+1/3-1/4+.+1/2008-1/2009
=1-1/2009
=2008/2009