解:(1)(5.6-1.6÷2)×2.5,
=(5.6-0.8)×2.5,
=4.8×2.5,
=1.2×4×2.5,
=1.2×(4×2.5),
=1.2×10,
=12;
(2)

×9-8÷

,
=

×9-8×

,
=

×(9-8),
=

×1,
=

;
(3)2001÷

,
=2001×

,
=2001×

,
=2001×(1+

),
=2001+

,
=2001+1

,
=2002

;
(4)

+

+

+…+

,
=

+

+

+…+

,
=(

+

+

+…+

)-(

+

+

+…+

),
=(

-

+

-

+

-

+…+

-

)-

×(

-

+

-

+

-

+…+

-

),
=(

-

)-

×(

-

),
=(

-

)×(1-

),
=

×

,
=

.
分析:(1)心酸括號(hào)內(nèi)的除法,再算括號(hào)內(nèi)的減法,原式變?yōu)?.8×2.5,把4.8變?yōu)?.2×4,運(yùn)用乘法結(jié)合律簡(jiǎn)算;
(2)把除法變?yōu)槌朔,運(yùn)用乘法分配律簡(jiǎn)算;
(3)把除法變?yōu)槌朔ǎ?999看作1998+1,運(yùn)用乘法分配律簡(jiǎn)算;
(4)因?yàn)槊總(gè)分?jǐn)?shù)分母中的兩個(gè)因數(shù)相差3,于是把原式變?yōu)?img class='latex' src='http://thumb.zyjl.cn/pic5/latex/221381.png' />+

+

+…+

,再把每個(gè)分?jǐn)?shù)拆分為兩個(gè)分?jǐn)?shù),原式變成(

+

+

+…+

)-(

+

+

+…+

),然后把每個(gè)分?jǐn)?shù)拆成兩個(gè)分?jǐn)?shù)相減的形式,進(jìn)一步求出結(jié)果.
點(diǎn)評(píng):對(duì)于簡(jiǎn)算的題目,就要注意觀察,認(rèn)真分析數(shù)字構(gòu)成的特點(diǎn)和規(guī)律,善于靈活運(yùn)用運(yùn)算定律或運(yùn)算技巧,巧妙解答.