1+2×3/1+3×4/1...202×203/1=多少?
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1+2×3/1+3×4/1...202×203/1=多少?
1×4/1+4×7/1+7×10/1+……+(3n-2)(3n-1)/1
1×4/1+4×7/1+7×10/1+……+(3n-2)(3n-1)/1
![1+2×3/1+3×4/1...202×203/1=多少?](/uploads/image/z/18459429-69-9.jpg?t=1%2B2%C3%973%2F1%2B3%C3%974%2F1...202%C3%97203%2F1%3D%E5%A4%9A%E5%B0%91%3F)
1/2×3=1/2-1/3=1/6
1/3×4=1/3-1/4=1/12
所以.原式=1+1/2-1/3+1/3-1/4+...1/202-1/203=1+1/2-1/203=607/406
再问: 1×4/1+4×7/1+7×10/1+……+(3n-2)(3n-1)/1
再答: 是+……+(3n-2)(3n+1)吧? 同样的展开方式。多除以3就行 1/(3n-2)(3n+1)={1/(3n-2)-1/(3n+1)}/3 所以1/1×4=(1-1/4)/3 1/4×7=(1/4-1/7)/3 原式={1-1/4+1/4-1/7+....+1/(3n-2)-1/(3n+1)}/3=n/(3n+1)
1/3×4=1/3-1/4=1/12
所以.原式=1+1/2-1/3+1/3-1/4+...1/202-1/203=1+1/2-1/203=607/406
再问: 1×4/1+4×7/1+7×10/1+……+(3n-2)(3n-1)/1
再答: 是+……+(3n-2)(3n+1)吧? 同样的展开方式。多除以3就行 1/(3n-2)(3n+1)={1/(3n-2)-1/(3n+1)}/3 所以1/1×4=(1-1/4)/3 1/4×7=(1/4-1/7)/3 原式={1-1/4+1/4-1/7+....+1/(3n-2)-1/(3n+1)}/3=n/(3n+1)