Question

小学奥数 简便运算 过程

1.（1+1/3）x（1—1/3）x（1+1/4）x（1—1/4）…（1+1/100）x（1—1/100） 2.1999+2000x1998/1999x2000-1
3.2002x1999-1957/42+1999x2001
4.1/2x4+1/4x6+1/8x10+1/10x12

Answer 1

1
分成两个式子，+号的和-号的分开来
（1+1/2）*（1+1/3）*(1+1/4)*……*(1+1/100)
=3/2*4/3*5/4*6/5*……*100/99+101/100=101/2
(前一个分子和后一个分母相消了)
减号的式*子同理
=1/2*2/3*3/4*……*98/99*99/100=1/100
（前一个分母和后一个分子相消了）
两个相乘等于101/200
2
(1999+2000x1998)/(1999x2000-1 )
=(1999+2000x1998)/(1998x2000+2000-1)
=(1999+2000x1998)/(1998x2000+1999)
=1
3
(2002x1999-1957)/(42+1999x2001)

=(2001x1999+1999-1957)/(42+1999x2001)
=(2001x1999+42)/(42+1999x2001)
=1
4
1/2x4+1/4x6+1/8x10+1/10x12
=(1/2-1/4+1/4-1/6+1/6-1/8+1/8-1/10+1/10-1/12)÷2
=（1/2-1/12）÷2
=5/12÷2
=5/24

Answer 2

.（1+1/3）x（1—1/3）x（1+1/4）x（1—1/4）…（1+1/100）x（1—1/100）
=4/3X2/3X5/4X3/4X6/5X4/5.....101/100X99/100
=2/3x101/100
= 202/300
2.1999+2000x1998/1999x2000-1
=1999+2000X(1999-1)/1999x2000-1
=1999+2000X1999-2000X1/1999x2000-1
=2000X1999-2000+1999/1999x2000-1
=2000X1999-1/1999x2000-1
=1
2002x1999-1957/42+1999x2001
=(2001+1)X1999-1957/42+1999x2001
=2001X1999+1999X1-1957/42+1999x2001
=2001X1999+1999-1957/42+1999x2001
=2001X1999+42/42+1999x2001
=1

Answer 3

先算第一道：原式＝4/3 * 2/3 * 5/4* 3/4 * 6/5 * 4/5 * .......* 101/100 * 99/100

= 2/3 * 101/100 = 202/300

Answer 4

要哪一题的简便运算