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

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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+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+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
1/2×3=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

请问是1+1/(2*3)+1/(3*4)....1/(202*203)吗?
1+1/(2*3)+...+1/(202*203)=1+1/2-1/3+1/3-1/4+......+1/202-1/203=1+1/2-1/203=607/406
1/(1*4)+1/(4*7)+...+1/(3n-2)(3n+1)
=3[1-1/4+1/4-1/7+....+1/(3n-2)-1...

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请问是1+1/(2*3)+1/(3*4)....1/(202*203)吗?
1+1/(2*3)+...+1/(202*203)=1+1/2-1/3+1/3-1/4+......+1/202-1/203=1+1/2-1/203=607/406
1/(1*4)+1/(4*7)+...+1/(3n-2)(3n+1)
=3[1-1/4+1/4-1/7+....+1/(3n-2)-1/(3n+1)]
=3[1-1/(3n+1)]
=9n/(3n+1)

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