有几道奥数题,要用简便计算(1)(1+1/2+1/3+1/4+...+1/9)*(1/2+1/3+1/4+...+1/1
1个回答

1.

设1/2+1/3+1/4+...+1/9=m

则原式= (1+m) X (m+0.1) -(1+0.1+m) X m

=m^2 +1.1m +0.1 - (m^2 +1.1m )

=0.1

2.

设 1/123456788=1/m

则原式[1/m - 1/(m+1) ] / [1/m + 1/(m+1) ]

=1/[m X (m+1)] / (123456788+123456789)/[m X (m+1)]

=1/246913577

3 . 原式= 91 X (2 X 11) X ( 3 X 9) X (4 X6) X (5 X 5 X2) X7 X 8 /

(22*24*25*27)

=91X7X8X2

=10192