(1/2根号1+根号2)+(1/3根号2+2根号3)+(1/4根号3+3根号4)……+(1/9根号8+8根号9)+(1/10根号9+9根号10)= 是1除以(2倍根号1+根号2)以此类推
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![(1/2根号1+根号2)+(1/3根号2+2根号3)+(1/4根号3+3根号4)……+(1/9根号8+8根号9)+(1/10根号9+9根号10)= 是1除以(2倍根号1+根号2)以此类推](/uploads/image/z/10233125-53-5.jpg?t=%EF%BC%881%2F2%E6%A0%B9%E5%8F%B71%2B%E6%A0%B9%E5%8F%B72%EF%BC%89%2B%EF%BC%881%2F3%E6%A0%B9%E5%8F%B72%2B2%E6%A0%B9%E5%8F%B73%EF%BC%89%2B%EF%BC%881%2F4%E6%A0%B9%E5%8F%B73%2B3%E6%A0%B9%E5%8F%B74%EF%BC%89%E2%80%A6%E2%80%A6%2B%281%2F9%E6%A0%B9%E5%8F%B78%2B8%E6%A0%B9%E5%8F%B79%29%2B%281%2F10%E6%A0%B9%E5%8F%B79%2B9%E6%A0%B9%E5%8F%B710%29%3D+%E6%98%AF1%E9%99%A4%E4%BB%A5%EF%BC%882%E5%80%8D%E6%A0%B9%E5%8F%B71%2B%E6%A0%B9%E5%8F%B72%EF%BC%89%E4%BB%A5%E6%AD%A4%E7%B1%BB%E6%8E%A8)
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(1/2根号1+根号2)+(1/3根号2+2根号3)+(1/4根号3+3根号4)……+(1/9根号8+8根号9)+(1/10根号9+9根号10)= 是1除以(2倍根号1+根号2)以此类推
(1/2根号1+根号2)+(1/3根号2+2根号3)+(1/4根号3+3根号4)……+(1/9根号8+8根号9)+(1/10根号9+9根号10)= 是1除以(2倍根号1+根号2)以此类推
(1/2根号1+根号2)+(1/3根号2+2根号3)+(1/4根号3+3根号4)……+(1/9根号8+8根号9)+(1/10根号9+9根号10)= 是1除以(2倍根号1+根号2)以此类推
第一项分子和分母都乘以根号1-根号2,第二项分子分母都乘以3根号2-2根号3,以此类推,下面就是平方差,可以化成非根号形式,化简得(2根号1-根号2)/2+)+(3根号2-2根号3)/6+.+(10根号9-9根号10)/90,继续化简,每项后面都与下一项前面的相消除,最后结果是1-根号10/10
有理化分母
(1-根号2/2)+(根号2/2-根号3/3)+(根号3/3-根号4/4)+....+(根号9/9-根号10/10)=1-根号10/10
有理化分母
(1-根号2/2)+(根号2/2-根号3/3)+(根号3/3-根号4/4)+....+(根号9/9-根号10/10)=1-根号10/10