1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512+1/1024=?

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1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512+1/1024=?1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512+1/

1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512+1/1024=?
1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512+1/1024=?

1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512+1/1024=?
1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512+1/1024
=1-1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512+1/1024
=1-1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512+1/1024
=...
=1-1/1024
=1023/1024

原式=1-1/2+1/2-1/4+1/4-1/8+1/8-1/16+1/16-1/32。。。。-1/1024
=1-1/1024
=1023/1024

Sn = a1(1-q^n)/(1-q)这个是公式
所以
原式=1/2(1-1/2^10)/(1-1/2)
=1023/1024