1/2+1/4+1/8，加1/16+1/32+1/64简便计算？

Question

如题所述

Answer 1

1/2+1/4+1/8+1/16+1/32+1/64
=1/2+1/4+1/8+1/16+1/32+(1/64+1/64)-1/64
=1/2+1/4+1/8+1/16+(1/32+1/32)-1/64
=1/2+1/4+1/8+(1/16+1/16)-1/64
=1/2+1/4+(1/8+1/8)-1/64
=1/2+(1/4+1/4)-1/64
=1/2+1/2-1/64
=1-1/64
=63/64
中间的过程可以略写的，只是为了让你方便理解，才一步步写出

Answer 2

原式=1/4+1/16+1/8+1/32+1/2+1/64=（16+4+8+2+32+1）/64=63/64.

Answer 3

1/2+1/4+1/8+1/16+1/32+1/64
=32/64+16/64+8/64+4/64+2/64+1/64
=63/64

Answer 4

等比数列求和公式1/2*（1-（1/2）^6）/（1-1/2）=63/64

Answer 5