用图形揭示计算的规律：二分之一加四分之一加八分之一加十六分之一… 二分之一加四分之一加八分之一加十六分之一简便计算
\u4e3a\u4ec0\u4e48\u8bd5\u56fe\u5229\u7528\u56fe\u5f62\u53cd\u6620\u7684\u89c4\u5f8b\u8ba1\u7b97\u4e8c\u5206\u4e4b\u4e00\u52a0\u56db\u5206\u4e4b\u4e00\u52a0\u516b\u5206\u4e4b\u4e00\u52a0\u5341\u516d\u5206\u4e4b\u4e00\u2026\u52a0\u4e8c\u7684n\u6b21\u65b9\u5206\u4e4b\u4e00\u7684\u503c\uff08\u4e8c\u5206\u4e4b\u4e00\u52a0\u56db\u5206\u4e4b\u4e00\u52a0\u516b\u5206\u4e4b\u4e00\u52a0\u5341\u516d\u5206\u4e4b\u4e00\u2026\u52a0\u4e8c\u7684n\u6b21\u65b9\u5206\u4e4b\u4e00
=1/2+1/4+1/8+1/16+......+1/2^(n-1)+1/2^n
=1/2+1/4+1/8+1/16+......+1/2^(n-1)+1/2^n+1/2^n-1/2^n
=1/2+1/4+1/8+1/16+......+1/2^(n-2)+1/2^(n-1)+1/2^(n-1)-1/2^n
=1/2+1/4+1/8+1/16+......+1/2^(n-2)+1/2^(n-2)-1/2^n
......
=1/2+1/4+1/8+1/16+1/32+1/32-1/2^n
=1/2+1/4+1/8+1/16+1/16-1/2^n
=1/2+1/4+1/8+1/8-1/2^n
=1/2+1/4+1/4-1/2^n
=1/2+1/2-1/2^n
=1-1/2^n
2\u5206\u4e4b1+4\u5206\u4e4b1+8\u5206\u4e4b1+16\u5206\u4e4b1
=\uff081-2\u5206\u4e4b1\uff09+\uff082\u5206\u4e4b1-4\u5206\u4e4b1\uff09+\uff084\u5206\u4e4b1-8\u5206\u4e4b1\uff09+\uff088\u5206\u4e4b1-16\u5206\u4e4b1\uff09
=1-2\u5206\u4e4b1+2\u5206\u4e4b1-4\u5206\u4e4b1+4\u5206\u4e4b1-8\u5206\u4e4b1+8\u5206\u4e4b1-16\u5206\u4e4b1
=1-16\u5206\u4e4b1
=16\u5206\u4e4b15
=(1-2分之1)+(2分之1-4分之1)+(4分之1-8分之1)+(8分之1-16分之1)+...(128分之1-256分之1)
=1-2分之1+2分之1-4分之1+...+128分之1-256分之1
=1-256分之1
=256分之255
二分之一加四分之一加八分之一加十六分之一…二百五六分之一
=(1-2分之1)+(2分之1-4分之1)+(4分之1-8分之1)+(8分之1-16分之1)+...(128分之1-256分之1)
=1-2分之1+2分之1-4分之1+...+128分之1-256分之1
=1-256分之1
=256分之255
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绛旓細1/2+1/4 =2/4+1/4 =3/4 鍏堢敤闃村奖閮ㄥ垎琛ㄧず鏁翠釜鍥惧舰鐨1/2锛屽啀鎶婄┖鐧介儴鍒(1/2)鐨1/2娑傛垚闃村奖锛岃繖鏍凤紝鍏ㄩ儴鐨勯槾褰遍儴鍒嗗氨鏄1/2+1/4鐨勫拰銆
