二分之一加四分之一加八分之一加16分之1加64分之1加128分之1等于 2分之1加4分之1加8分之1加16分之1加32分之1加64分...
4\u5206\u4e4b1\u52a08\u5206\u4e4b1\u52a016\u5206\u4e4b1\u52a032\u5206\u4e4b1\u52a064\u5206\u4e4b1\u52a0128\u5206\u4e4b1\u7b80\u4fbf\u8ba1\u7b971/4+1/8+1/16+1/32+1/64+1/128=127/128
\u56e0\u4e3a\u6bcf\u4e00\u9879\u540e\u9762\u7684\u5206\u6bcd\u90fd\u662f\u524d\u9762\u7684\u4e00\u534a,\u6240\u4ee5\u4f60\u53ef\u4ee5\u5728\u539f\u6765\u7684\u5f0f\u5b50\u6700\u540e+1/128,\u53ef\u4ee5\u53d1\u73b0\u4ece\u540e\u5f80\u524d\u7b97,\u5c31\u662f2\u4e2a1/128\u52a0\u8d77\u6765\u53d8\u62101\u4e2a1/64,\u7136\u540e2\u4e2a1/64\u52a0\u8d77\u6765\u53d8\u62101\u4e2a1/32,\u4f9d\u6b21\u7c7b\u63a8,...\u6700\u540e\u5c31\u662f2\u4e2a1/2\u52a0\u8d77\u6765\u53d8\u62101.
\u6240\u4ee5\u4f60\u5176\u5b9e\u53ea\u8981\u5c061-1/128=127/128\u5373\u53ef.
\u4e8c\u5206\u4e4b\u4e00\u52a0\u56db\u5206\u4e4b\u4e00\u52a0\u516b\u5206\u4e4b\u4e00\u52a0\u5341\u516d\u5206\u4e4b\u4e00\u52a0\u4e09\u5341\u4e8c\u5206\u4e4b\u4e00\u52a0\u516d\u5341\u56db\u5206\u4e4b\u4e00
=64\u5206\u4e4b1\u4e5832+64\u5206\u4e4b1\u4e5816+64\u5206\u4e4b1\u4e588+64\u5206\u4e4b1\u4e584+64\u5206\u4e4b1\u4e582+64\u5206\u4e4b1
=64\u5206\u4e4b1\u4e58\uff0832+16+8+4+2+1\uff09
=64\u5206\u4e4b1\u4e5863
=64\u5206\u4e4b63
=64/128+32/168+16/128+8/128+1/128
=121/128
绛旓細瑙ｏ細浜屽垎涔嬩竴鍔犲洓鍒嗕箣涓鍔犲叓鍒嗕箣涓鈥︹﹀姞涓鐧句簩鍗佸叓鍒嗕箣涓 =1/2+1/4+1/8+鈥︹+1/128 =(1-1/2)+(1/2-1/4)+(1/4-1/8)+鈥︹+(1/64-1/128)=1-1/2+1/2-1/4+1/4-1/8+鈥︹+1/64-1/128 锛堜腑闂翠袱椤逛负涓缁勭浉鍔犲垰濂戒负0鎶垫秷浜嗭級=1-1/128 =127/128 ...
绛旓細浜屽垎涔嬩竴鍔犲洓鍒嗕箣涓鍔犲叓鍒嗕箣涓鍔鍗佸叚鍒嗕箣涓鍔犱笁鍗佷簩鍒嗕箣涓 1锛2鍗1锛4鍗1锛8鍗1锛16鍗1锛32锛濓紙1锛2x锛1涓锛1锛2锛夛季5锛夛級锛1涓1锛2 锛濓紙1锛2x锛1涓1锛32锛夛紡1锛2 锛1涓1锛32 锛31锛32
绛旓細锛1锛夌敤绠渚挎柟娉曡绠楋細2鍒嗕箣1+4鍒嗕箣1+8鍒嗕箣1+16鍒嗕箣1+32鍒嗕箣1+64鍒嗕箣1+128鍒嗕箣1+256鍒嗕箣1 1/2+1/4+1/8...+1/256 =(128+64+32...+1)/256 =255/256 2鍒嗕箣1+4鍒嗕箣1+8鍒嗕箣1+16鍒嗕箣1+32鍒嗕箣1+64鍒嗕箣1 瑙ｆ硶涓锛氬師寮=1/2+1/4+1/8+1/16+1/32+(1/64+1...
绛旓細浣犲ソ锛浜屽垎涔嬩竴锛鍥涘垎涔嬩竴锛鍏垎涔涓+...+浜岀櫨浜斿崄鍏垎涔嬩竴 =锛1-1/2锛+锛1/2-1/4锛+锛1/4-1/8锛+鈥︹+锛1/128-1/256锛=1-1/2+1/2-1/4+1/4-1/8+1/8-鈥︹-1/128+1/128-1/256 =1-1/256 =255/256
绛旓細鍒嗘瀽锛氬厛閫氬垎锛屽彉鎴愬悓鍒嗘瘝鐨勫垎鏁扮浉鍔犲氨鍙互浜嗐傝В锛½锛¼锛1/8+1/16+1/32+1/64+1/128 =64/128+32/128+16/128+8/12+4/128+2/128+1/128 =锛64+32+16+8+4+2+1锛/128 =127/128 锛堢粨鏋滄槸128鍒嗕箣127锛
绛旓細浜屽垎涔嬩竴鍔犲洓鍒嗕箣涓鍔犲叓鍒嗕箣涓 =鍏垎涔(4+2+1)=鍏垎涔嬩竷
绛旓細瑙ｏ細浠=1/2+1/4+1/8+1/16+...+1/2^n 鈶犱箻浠1/2鍒欐湁1/2S=1/4+1/8+1/16...+1/2^(n+1) 鈶♀憼-鈶″緱S-1/2S=1/2-1/2^(n+1)1/2S=1/2-1/2^(n+1)鍗砈=1-1/2^n
绛旓細閫氬垎涔熷お楹荤儲浜嗗惂锛屾妸鎵鏈夊垎鏁颁箻浜岋紝灏卞彉鎴愨1+浜屽垎涔嬩竴鍔犲洓鍒嗕箣涓鍔犲叓鍒嗕箣涓鈥︹﹀姞涓夊崄浜屽垎涔嬩竴鈥濈敤1鍑忓幓鍏崄鍥涘垎涔嬩竴绛変簬鍏崄鍥涘垎涔嬪叚鍗佷笁OK浜
绛旓細浜屽垎涔嬩竴鍔犲洓鍒嗕箣涓鍔犲叓鍒嗕箣涓鍔鍗佸叚鍒嗕箣涓鈥︿簩鐧句簲鍏垎涔嬩竴 =(1-2鍒嗕箣1)+(2鍒嗕箣1-4鍒嗕箣1)+(4鍒嗕箣1-8鍒嗕箣1)+(8鍒嗕箣1-16鍒嗕箣1)+...(128鍒嗕箣1-256鍒嗕箣1)=1-2鍒嗕箣1+2鍒嗕箣1-4鍒嗕箣1+...+128鍒嗕箣1-256鍒嗕箣1 =1-256鍒嗕箣1 =256鍒嗕箣255 ...
绛旓細1/2+1/4+1/8+1/16+1/32+1/64=(32+16+8+4+2+1)/64=63/64
