关于有理数运算的数学题求和 (1/1+2)+(1/1+2+3)+(1/1+2+3+4)+……=(1/1+2+3+……n)啊上面那个等号错了正确的应该是这个 求和 (1/1+2)+(1/1+2+3)+(1/1+2+3+4)+……+(1/1+2+3+……n)
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![关于有理数运算的数学题求和 (1/1+2)+(1/1+2+3)+(1/1+2+3+4)+……=(1/1+2+3+……n)啊上面那个等号错了正确的应该是这个 求和 (1/1+2)+(1/1+2+3)+(1/1+2+3+4)+……+(1/1+2+3+……n)](/uploads/image/z/386345-65-5.jpg?t=%E5%85%B3%E4%BA%8E%E6%9C%89%E7%90%86%E6%95%B0%E8%BF%90%E7%AE%97%E7%9A%84%E6%95%B0%E5%AD%A6%E9%A2%98%E6%B1%82%E5%92%8C+%EF%BC%881%2F1%2B2%EF%BC%89%2B%EF%BC%881%2F1%2B2%2B3%EF%BC%89%2B%281%2F1%2B2%2B3%2B4%29%2B%E2%80%A6%E2%80%A6%3D%281%2F1%2B2%2B3%2B%E2%80%A6%E2%80%A6n%29%E5%95%8A%E4%B8%8A%E9%9D%A2%E9%82%A3%E4%B8%AA%E7%AD%89%E5%8F%B7%E9%94%99%E4%BA%86%E6%AD%A3%E7%A1%AE%E7%9A%84%E5%BA%94%E8%AF%A5%E6%98%AF%E8%BF%99%E4%B8%AA+%E6%B1%82%E5%92%8C+%EF%BC%881%2F1%2B2%EF%BC%89%2B%EF%BC%881%2F1%2B2%2B3%EF%BC%89%2B%281%2F1%2B2%2B3%2B4%29%2B%E2%80%A6%E2%80%A6%2B%281%2F1%2B2%2B3%2B%E2%80%A6%E2%80%A6n%29)
关于有理数运算的数学题求和 (1/1+2)+(1/1+2+3)+(1/1+2+3+4)+……=(1/1+2+3+……n)啊上面那个等号错了正确的应该是这个 求和 (1/1+2)+(1/1+2+3)+(1/1+2+3+4)+……+(1/1+2+3+……n)
关于有理数运算的数学题
求和 (1/1+2)+(1/1+2+3)+(1/1+2+3+4)+……=(1/1+2+3+……n)
啊上面那个等号错了
正确的应该是这个 求和 (1/1+2)+(1/1+2+3)+(1/1+2+3+4)+……+(1/1+2+3+……n)
关于有理数运算的数学题求和 (1/1+2)+(1/1+2+3)+(1/1+2+3+4)+……=(1/1+2+3+……n)啊上面那个等号错了正确的应该是这个 求和 (1/1+2)+(1/1+2+3)+(1/1+2+3+4)+……+(1/1+2+3+……n)
等差数列前n项求和公式:Sn=n(n+1)/2,则原式=2/(2*3)+2/(3*4)+……+2/(n*(n+1))=2*(1/(2*3)+1/(3*4)+……+1/(n*(n+1))=2*(1/2-1/3+1/3-1/4+……+1/n-1/(n+1))=2*(1/2-1/(n+1))=(n-1)/(n+1)
原式=2/(2×3)+2/(3×4)+...+2/n*(n+1)
=2[(1/2-1/3)+(1/3-1/4)+...+1/n-1/(n+1)]
=2(1/2-1/(n+1)]
=(n-1)/(n+1)
当 n 趋于无穷时为 1
上面的式子可以写成
2/2(1+2)+2/3(1+3)+....+2/n(1+n)=
2[1/2x3+1/3x4+1/4x5....1/n(n+1)]=
2[1/2-1/3+1/3-1/4+.....+1/n-1/n+1]=
2(1/2-1/n+1)=n-1/n+1
n=2,3,4,5......