问题 填空题

计算:l×2+2×3+3×4+…+28×29+29×30=______.

答案

l×2+2×3+3×4+…+28×29+29×30,

=1×(1+1)+2×(1+2)+3×(1+3)+…28×(1+28)+29×(1+29),

=1+1×1+2+2×2+3+3×3+…28+28×28+29+29×29,

=(1+2+3+…28+29)+(1×1+2×2+3×3+…28×28+29×29),

=(1+29)×29÷2+29(29+1)(2×29+1)÷6,

=435+8555,

=8990;

故答案为:8990.

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