1. 计算下面各题。
(1) $4.2×5+40.02×5+400.002×5+4000.0002×5+40000.00002×5$
(2) $(1.5+2.5+\dots+2026.5)×(2.5+3.5+\dots+2027.5)-(1.5+2.5+\dots+2027.5)×(2.5+3.5+\dots+2026.5)$

1.(1)原式=(4+0.2)×5+(40+0.02)×5+(400+0.002)×5+(4000+0.0002)×5+(40000+0.00002)×5
=(20+200+2000+20000+200000)+(1+0.1+0.01+0.001+0.0001)
=222220+1.1111
=222221.1111
(2)设a=1.5+2.5+…+2026.5,b=2.5+3.5+…+2026.5,则a-b=1.5,
原式=a×(b+2027.5)-(a+2027.5)×b
=ab+2027.5a-ab-2027.5b
=2027.5×(a-b)
=2027.5×1.5
=3041.25

2. 用两种方法计算:$888···8.8×999···9.9$。
2026个8
2026个9

2. 方法一：
$\underbrace{888···8}_{2026个8}.8 × \underbrace{999···9}_{2026个9}.9$
$=\underbrace{888···8}_{2026个8}.8 × (\underbrace{1\ 000···0}_{2026个0}-0.1)$
$=\underbrace{888···8}_{2027个8}\underbrace{000···0}_{2025个0}-\underbrace{888···8}_{2025个8}.88$
$=\underbrace{888···8}_{2026个8}7 \underbrace{111···1}_{2025个1}.12$
方法二：
8.8×9.9=87.12
88.8×99.9=8871.12
888.8×999.9=888711.12
所以$\underbrace{888···8}_{n个8}.8 × \underbrace{999···9}_{n个9}.9 = \underbrace{888···8}_{n个8}7 \underbrace{111···1}_{(n-1)个1}.12$
因此,原式=$\underbrace{888···8}_{2026个8}7 \underbrace{111···1}_{2025个1}.12$
提示:可以将$\underbrace{999···9}_{2026个9}.9$看作$\underbrace{1\ 000···0}_{2026个0}-0.1$来计算,也可以用归纳法得出规律后直接写出结果。