巧算1/1×2+1/2×3+1/3×4+…1/49×50
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巧算1/1×2+1/2×3+1/3×4+…1/49×50巧算1/1×2+1/2×3+1/3×4+…1/49×50巧算1/1×2+1/2×3+1/3×4+…1/49×501/1×2+1/2×3+1/3×
巧算1/1×2+1/2×3+1/3×4+…1/49×50
巧算1/1×2+1/2×3+1/3×4+…1/49×50
巧算1/1×2+1/2×3+1/3×4+…1/49×50
1/1×2+1/2×3+1/3×4+…1/49×50
=1-1/2+1/2-1/3+…+1/49-1/50
=1-1/50
=49/50
1/1×2+1/2×3+1/3×4+…1/49×50
规律是:
利用“欧拉公式”(可以查阅相关书籍):1+1/2+1/3+……+1/n=ln(n)+C,C为欧拉常数 数值是0.5772
=(1+1/1)+(1+1/2).............+(1+1/n)
=n+ln(n)+C
=49.5772+ln49
或者,如果是这样书写1/(1×2)+.....
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1/1×2+1/2×3+1/3×4+…1/49×50
规律是:
利用“欧拉公式”(可以查阅相关书籍):1+1/2+1/3+……+1/n=ln(n)+C,C为欧拉常数 数值是0.5772
=(1+1/1)+(1+1/2).............+(1+1/n)
=n+ln(n)+C
=49.5772+ln49
或者,如果是这样书写1/(1×2)+........+1/(49x50)
1/1×2+1/2×3+1/3×4+…1/49×50
=(1-1/2)+(1/2-1/3)+…+(1/49-1/50)
=1-1/50
=49/50
两种不一样。
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