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分之1简便计算
1/2+1/4+1/8+1/16+1/32+1/64=(1/2+1/4+1/8+1/16+1/32+1/64+1/64)-1/64
=1-1/64
=63/64
用借一换一的方法,先借一个1/64,然后用括号括起来,先后算括号,从后面算来,1/64+1/64=1/32,1/32+1/32=1/16,1/16+1/16=1/8,由此类推,最后是1/2+1/2=1,然后就是1-1/64=63/64了.再教你一个方法,如果前一个数是后一个数的两倍,而且还是加号,就可以用第一个分数的两倍减去最后一个分数.
1/2+1/4+1/8+1/16+1/32+1/64
=1/2×2-1/64
=63/64
绛旓細2鍒嗕箣1鍔4鍒嗕箣1鍔8鍒嗕箣1.鍔256鍒嗕箣1 =1/2脳[1-(1/2)^8]/(1-1/2)=1-(1/2)^8 =1-1/256 =255/256 锛256鍒嗕箣255锛
绛旓細璁＄畻杩囩▼濡備笅锛1/2+1/4+1/8+1/16+...+1/128 =1-1/2+1/2-1/4+1/4-1/8+1/8-1/16+...+1/64-1/128 =1-1/128锛堢敱涓婁竴姝ョ害鎺夛級=127/128
绛旓細1/16=1/8-1/16 浜屽垎涔嬩竴鍔犲洓鍒嗕箣涓鍔犲叓鍒嗕箣涓鍔犲崄鍏垎涔嬩竴 =1-1/2+1/2-1/4+1/4-1/8+1/8-1/16 =1-1/16 =15/16 鍒嗘暟琛ㄧず涓涓暟鏄彟涓涓暟鐨勫嚑鍒嗕箣鍑狅紝鎴栦竴涓簨浠朵笌鎵鏈変簨浠剁殑姣斾緥銆傛妸鍗曚綅鈥1鈥濆钩鍧囧垎鎴愯嫢骞蹭唤锛岃〃绀鸿繖鏍风殑涓浠芥垨鍑犱唤鐨勬暟鍙垎鏁般傚垎瀛愬湪涓婏紝鍒嗘瘝鍦ㄤ笅銆
绛旓細浜屽垎涔嬩竴鍔犲洓鍒嗕箣涓鍔犲叓鍒嗕箣涓鍔犲崄鍏垎涔嬩竴...=1/2+1/4+1/8+1/16...=3/4+1/8+1/16...=7/8+1/16鈥︹=15/16鈥︹
绛旓細1/2+1/4=1/1/4=3/4 1/2+1/4+1/8=1-1/8=7/8 鈥︹2鍒嗕箣1鍔4鍒嗕箣涓鍔8鍒嗕箣涓鍔16鍒嗕箣涓鍔犲埌2048鍒嗕箣涓=1-1/2048=2047/2048
绛旓細1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256 =1-1/256 =255/256
绛旓細绠渚胯繍绠楋細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= 鐢辩瓑姣旀暟鍒楁眰鍜屽緱锛歋n=[锛1/2锛-锛1/64锛*锛1/2锛塢/[1-锛1/2锛塢=63/64 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=锛 锛 2鍒嗕箣1+4鍒嗕箣1+8鍒嗕箣1+...
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犲崄鍏垎涔嬩竴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
