Question

1/2+1/4+1/8+1/16+1/32+1/64+1/128等于？为什么

Answer 1

设1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256=a
两边同时×1/2
得
1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512=1/2a
a-1/2a
=1/2-1/512
=255/512
=1/2a
a=255/256

Answer 2

1/2+1/4+1/8+1/16+1/32+1/64+1/128=127/128
因为1/2=1-1/2
1/4=1/2-1/4
……
所以1/2+1/4+1/8+1/16+1/32+1/64+1/128
=1-1/2+1/2-1/4+1/4-1/8+1/8-1/16+1/16-1/32+1/32-1/64+1/64-1/128
=1-(1/2+1/2)-(1/4+1/4)-(1/8+1/8)-(1/16+1/16)-(1/32+1/32)-(1/64+1/64)-1/128
=1-1/128
=127/128

Answer 3

1/2+1/4+1/8+1/16+1/32+1/64+1/128
=(1-1/2)+(1/2-1/4)+(1/4-1/8)+……+(1/64-1/128)
=1-1/128=127/128