2/1*(1+2)+3/(1+2)*(1+2+3)+4/(1+2+3)*(1+2+3+4)+...+(1+2+3+...+99)*(1+2+...+100)是多少,
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/03 10:43:10
![2/1*(1+2)+3/(1+2)*(1+2+3)+4/(1+2+3)*(1+2+3+4)+...+(1+2+3+...+99)*(1+2+...+100)是多少,](/uploads/image/z/10922085-45-5.jpg?t=2%2F1%2A%281%2B2%29%2B3%2F%281%2B2%29%2A%281%2B2%2B3%29%2B4%2F%281%2B2%2B3%29%2A%281%2B2%2B3%2B4%29%2B...%2B%281%2B2%2B3%2B...%2B99%29%2A%281%2B2%2B...%2B100%29%E6%98%AF%E5%A4%9A%E5%B0%91%2C)
2/1*(1+2)+3/(1+2)*(1+2+3)+4/(1+2+3)*(1+2+3+4)+...+(1+2+3+...+99)*(1+2+...+100)是多少,
2/1*(1+2)+3/(1+2)*(1+2+3)+4/(1+2+3)*(1+2+3+4)+...+(1+2+3+...+99)*(1+2+...+100)是多少,
2/1*(1+2)+3/(1+2)*(1+2+3)+4/(1+2+3)*(1+2+3+4)+...+(1+2+3+...+99)*(1+2+...+100)是多少,
方法:裂项法
2/1×(1+2)+3/(1+2)(1+2+3)+4/(1+2+3)(1+2+3+4)+.+100/(1+2+..+99)(1+2+..+100)
=[1-1/(1+2)]+[1/(1+2)-1/(1+2+3)]+[1/(1+2+3)-1/(1+2+3+4)]+.+[1/(1+2+..+99)-1/(1+2+..+100)]
=1-1/(1+2+...+100)
=1-1/5050
=5049/5050.