Question

小学六年级奥数题（简便运算）

1997 X 0.3 1.2
————— + ——
1999 X 0.5 1999

1 1 1 1 1
—————— + —————— + —————— + —————— + ——
1986 X 1987 1987 X 1988 1988 X1989 1989 X 1990 1990

Answer 1

第一题：
1997X0.3 1.2 1997 X 0.3 1.2 X 0.5 1997X0.3 + 4 X0.3X0.5
———— + -——＝------------- + ----------- =-----------------------
1999X0.5 1999 1999 X 0.5 1999 X 0.5 1999 X 0.5
(1997+4X0.5)X0.3 1999X0.3 0.3 3
=---------------------- = -------------- = --------- = ---
1999X0.5 1999X0.5 0.5 5

第二题：（从最后一步往前算）
1 1 1989 1
其一：------- + ------------- = ---------------- + -------------
1990 1989 X 1990 1989 X 1990 1989 X 1990

1989 + 1 1990 1
= --------------- = -------------- = -----------
1989 X 1990 1989 X 1990 1989

1 1 1
其二(继续往前面加)：---------------- + --------- ＝ --------
1988 X 1989 1989 1988

照此规律，可以得出，最后的结果应该是：
1
-----------
1986

Answer 2

由1/(1986*1987)=1/1986-1/1987的规律，得到，第二式＝1/1986-1/1991

Answer 3

1/(1986x1987)+1/(1987x1988)+1/(1988x1999)

+1/1990

解：原式可化为

(1/1986-1/1987)+(1/1987-1/1988)+(1/1988-
1/1999)+1/1999

=1/1986-1/1987+1/1987-1/1988+1/1988-

1/1999+1/1999

=1/1999

Answer 4

1
-----------
1986

Answer 5

1/1*3+1/3*5+1/5*7+……+1/47*49
=
1/2(1-1/3)+........1/2(1/47-1/49)
=
1/2(1-1/3+1/3-1/5+.......+1/47-1/49)
=24/49
1/2*5+1/3*5+1/8*11+……+1/20*23
=
=
3/4+7/12-9/20+11/30-13/42
=(1-1/4+1/4+1/3-1/4-1/5+1/5+1/6-1/6-1/7)
=
1+1/3-1/4-1/7
=79/84
2002/1*3+2002/3*5+2002/5*7+2002/7*9+2002/9*11
=2002(1/1*3+1/3*5+...+1/9*11)
=2002[1/2(1-1/3)+1/2(1/3-1/5)+...+1/2(1/9-1/11)
=2002*5/11
=910

Answer 6

老天!哪儿来的题啊！