1/2+1/4+1/8+1/16+...+1/n
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1/2+1/4+1/8+1/16+...+1/n1/2+1/4+1/8+1/16+...+1/n1/2+1/4+1/8+1/16+...+1/n令t=1/2+1/4+1/8+1/16+...+1/2^
1/2+1/4+1/8+1/16+...+1/n
1/2+1/4+1/8+1/16+...+1/n
1/2+1/4+1/8+1/16+...+1/n
令t=1/2+1/4+1/8+1/16+...+1/2^n
t/2=1/4+1/8+1/16+...+1/2^(n+1)
t-t/2=1/2-1/2^(n+1)
t/2=1/2-1/2^(n+1)
t=1-1/2^n
即1/2+1/4+1/8+1/16+...+1/2^n=1-1/2^n