数学题:1/2+1/4+1/8+1/16+.+1/2n(n=10)
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数学题:1/2+1/4+1/8+1/16+.+1/2n(n=10)
数学题:1/2+1/4+1/8+1/16+.+1/2n(n=10)
数学题:1/2+1/4+1/8+1/16+.+1/2n(n=10)
令S=1/2+1/4+1/8+1/16+.+1/2^10
2S=1+1/2+1/4+1/8+1/16+.+1/2^8+1/2^9
2S-S=1-1/2^10
S=1-1/2^10
原式=1/2+1/4+1/8+...+1/2^10
=1/2+1/4+1/8+...+1/2^10+1/2^10-1/2^10
...
...
=1-1/2^10
=1023/1024