Question

小学六年级奥数题及答案

简便运算
20-5/2-9/4-17/8-33/16-65/32-129/64
20-2*+1/2-2*4+1/4-8*2+1/8-16*2+1/16-----64*2+1/64
20-2*6-1/2-1/4-1/8-----1/64
8-(32+16+8+4+2+1/64)
8-63/64
7+1/64

Answer 1

20-5/2-9/4-17/8-33/16-65/32-129/64
=20-2-1/2-2-1/4-2-1/8-2-1/16-2-1/32-2-1/64
=20-2*6-(1/2+1/4+1/8+1/16+1/32+1/64)
=8-63/64
=7又1/64
（说明最后加一个1/64又减去一个1/64，利用倒推法得出1/2+1/4+1/8+1/16+1/32+1/64=1-1/64=63/64）

Answer 2

20-5/2-9/4-17/8-33/16-65/32-129/64
=20 - 2又1/2 - 2又1/4 - 2又1/8 - 2又1/16 - 2又1/32 - 2又1/64
=20-2*6-(1/2+1/4+1/8+1/16+1/32+1/64)
=20-2*6-（1-1/2）+(1/2-1/4)+(1/4-1/8)+(1/8-1/16)+(1/16-1/32)+(1/32-1/64)
=8-(1-1/64)
=7又1/64

Answer 3