两道小学简算 求解

2:=1(1-1/2)*2*(1-1/3)*3*(1-1/4)*4*(1-1/5)*5*(1-1/6)*6*(1-1/7)*7*(1-1/8)*8*(1-1/9)*9*(1-1/10)
=1x2x3x4x5x6x7x8x9x1/2x2/3x3/4x4/5x5/6x6/7x7/8x8/9x9/10
=2x3x4x5x6x7x8x9x1/10
=3x4x6x7x8x9
36288

2、

原式=(1×1/2)×(2×2/3)×(3×3/4)×(4×4/5)×(5×5/6)×(6×6/7)×(7×7/8)×(8×8/9)×(9×9/10)

=(1×2×3×4×5×6×7×8×9)×(1/2×2/3×3/4×4/5×5/6×6/7×7/8×8/9×9/10)

=362880×1/10

=36288

3、错位相减法

S=          3/4+4/8+5/16+6/32+7/64+8/128+9/256

2S=3/2+4/4+5/8+6/16+7/32+8/64+9/128

相减得到：

S=3/2+1/4+1/8+1/16+1/32+1/64+1/128-9/256

=3/2+(1/2-1/4)+(1/4-1/8)+(1/8-1/16)+(1/16-1/32)+(1/32-1/64)+(1/64-1/128)-9/256

=2-1/128-9/256

=1又245/256