1/2,1/6,1/12,1/20,1/30……100个数相加是多少
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![1/2,1/6,1/12,1/20,1/30……100个数相加是多少](/uploads/image/z/8665177-49-7.jpg?t=1%2F2%2C1%2F6%2C1%2F12%2C1%2F20%2C1%2F30%E2%80%A6%E2%80%A6100%E4%B8%AA%E6%95%B0%E7%9B%B8%E5%8A%A0%E6%98%AF%E5%A4%9A%E5%B0%91)
1/2,1/6,1/12,1/20,1/30……100个数相加是多少
1/2,1/6,1/12,1/20,1/30……100个数相加是多少
1/2,1/6,1/12,1/20,1/30……100个数相加是多少
1/2+1/6+1/12+.+1/(100×101)
=1/2+1/2-1/3+1/3-1/4+...+1/100-1/101
=1-1/101
=100/101
1/2+1/6+...+1/100*101
=1/1/2+1/2-1/3+..+1/100-1/101
=1-1/101
=100/101
1/2+1/6+1/12+1/20+1/30+...=1/(1×2)+1/(2×3)+1/(3×4)+。。。+1/(100×101)
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+。。。+(1/99-1/100)+(1/100-1/101)
=1-1/101
=100/101