1x1!+2x2!+3x3!+.2008x2008!=

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1x1!+2x2!+3x3!+.2008x2008!=1x1!+2x2!+3x3!+.2008x2008!=1x1!+2x2!+3x3!+.2008x2008!=n*n!=[(n+1)-1]*n!=(

1x1!+2x2!+3x3!+.2008x2008!=
1x1!+2x2!+3x3!+.2008x2008!=

1x1!+2x2!+3x3!+.2008x2008!=
n*n!
=[(n+1)-1]*n!
=(n+1)*n!-1*n!
=(n+1)!-n!
所以原式=2!-1!+3!-2!+……+2009!-2008!
=2009!-1

换底公式
loga(b)=lgb/lga=lnb/lna
154=2×7×11
所以分别是2,7,11
√a²=|a|
所以原式=|0.388|+|0.603|
=0.388+0.603
=0.991