(1+0.3+0.31+0.32……+0.39)×(0.3+0.31+0.32+……+0.39+0.4)-(1+0.3+0.31+0.32……+0.39+0.4)×(0.3+0.31+0.32+……+0.39)=

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(1+0.3+0.31+0.32……+0.39)×(0.3+0.31+0.32+……+0.39+0.4)-(1+0.3+0.31+0.32……+0.39+0.4)×(0.3+0.31+0.32+……+

(1+0.3+0.31+0.32……+0.39)×(0.3+0.31+0.32+……+0.39+0.4)-(1+0.3+0.31+0.32……+0.39+0.4)×(0.3+0.31+0.32+……+0.39)=
(1+0.3+0.31+0.32……+0.39)×(0.3+0.31+0.32+……+0.39+0.4)-(1+0.3+0.31+0.32……+0.39+0.4)×(0.3+0.31+0.32+……+0.39)=

(1+0.3+0.31+0.32……+0.39)×(0.3+0.31+0.32+……+0.39+0.4)-(1+0.3+0.31+0.32……+0.39+0.4)×(0.3+0.31+0.32+……+0.39)=
技巧:巧用乘法分配率.
在式子中+0.4×(0.3+0.31+……+0.39+0.4),再-0.4×(0.3+0.31+……+0.39+0.4)
原式=(1+0.3+0.31+0.32……+0.39)×(0.3+0.31+0.32+……+0.39+0.4)+0.4×(0.3+0.31+……+0.39+0.4)-(1+0.3+0.31+0.32……+0.39+0.4)×(0.3+0.31+0.32+……+0.39)-0.4×(0.3+0.31+……+0.39+0.4)
乘法分配率得
原式=(1+0.3+0.31+0.32……+0.39+0.4)×(0.3+0.31+0.32+……+0.39+0.4)-(1+0.3+0.31+0.32……+0.39+0.4)×(0.3+0.31+0.32+……+0.39)-0.4×(0.3+0.31+……+0.39+0.4)
再次运用乘法分配率得
原式=(1+0.3+0.31+0.32……+0.39+0.4)×0.4-0.4×(0.3+0.31+……+0.39+0.4)
再次运用乘法分配率得
原式=1×0.4
=0.4

希望对你解题有所帮助

(1+0.3+0.31+0.32……+0.39)×(0.3+0.31+0.32+……+0.39+0.4)-(1+0.3+0.31+0.32……+0.39+0.4)×(0.3+0.31+0.32+……+0.39)
=(1+0.3+0.31+0.32……+0.39)×(0.3+0.31+0.32+……+0.39)+(1+0.3+0.31+0.32……+0.39)×0.4-(1+0.3+0.31...

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(1+0.3+0.31+0.32……+0.39)×(0.3+0.31+0.32+……+0.39+0.4)-(1+0.3+0.31+0.32……+0.39+0.4)×(0.3+0.31+0.32+……+0.39)
=(1+0.3+0.31+0.32……+0.39)×(0.3+0.31+0.32+……+0.39)+(1+0.3+0.31+0.32……+0.39)×0.4-(1+0.3+0.31+0.32……+0.39)×(0.3+0.31+0.32+……+0.39)-0.4×(0.3+0.31+0.32……+0.39)
=0.4+(0.3+0.31+0.32……+0.39)×0.4-0.4×(0.3+0.31+0.32……+0.39)
=0.4

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(1+0.3+0.31+0.32……+0.39)×[(0.3+0.31+0.32+……+0.39+0.4)-(0.3+0.31+0.32+……+0.39)]
=(1+0.3+0.31+0.32……+0.39) x 0.1
= (1 + 0.3 x 10 + 0.01 + 0.02...+0.09) x 0.1
= (4 + 0.55 ) x 0.1
= 0.455

设x=1+0.3+0.31+0.32……+0.39。得:
X(X-0.6)-(X+0.4)(X-1)
=X^2-0.6X-(X^2-0.6X-0.4)
=0.4

0.30+0.31+0.32+...+0.39+0.4+0.35=0.7*10/2=3.5
上式=(3.5+1-0.35-0.4)*(3.5-0.35)-(1+3.5-0.35)*(3.5-0.4-0.35)=

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