简算1/2+1/4+1/8+.+1/256并写出为什么!

简算1/2+1/4+1/8+.+1/256
并写出为什么!

1/2+1/4+1/8+.+1/64+1/128+1/256
=1/2+1/4+1/8+.+1/64+1/128+1/256+1/256-1/256
=1/2+1/4+1/8+.+1/64+1/128+1/128-1/256
=1/2+1/4+1/8+.+1/64+1/64-1/256
=1/2+1/4+1/8+..+1/32+1/32-1/256
..
=1/2+1/2-1/256
=1-1/256
=255/256
明教为您解答,
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祝您学业进步!

等比数列求和公式带一下就完事了啊。。。