Question

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

Answer 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

追问

1×4/1+4×7/1+7×10/1+……+（3n-2)(3n-1)/1

追答

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)

Answer 2

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)

追问

1×4/1+4×7/1+7×10/1+……+（3n-2)(3n-1)/1

追答

是(3n+1)，不是(3n-1)

追问

嗯回答呢

追答

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)