0.999锟斤拷锟斤拷1谁锟斤拷0.999锟斤拷锟斤拷锟斤拷1锟斤拷

锟斤拷锟斤拷时锟戒：2024-03-30 12:37:50 锟斤拷锟斤拷锟� 锟斤拷要投锟斤拷

"0.666...锟斤拷2/3谁锟斤拷锟斤拷说锟金案ｏ拷0.666...锟斤拷2/3一锟斤拷锟斤拷0.666...=2/3锟斤拷锟斤拷锟斤拷锟侥匡拷毯锟斤拷锟斤拷锟窖э拷募锟斤拷锟剿硷拷锟斤拷锟斤拷""0.666...锟斤拷2/3锟侥革拷锟斤拷?""锟杰讹拷锟剿伙拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷循锟斤拷小锟斤拷锟斤拷位锟斤拷锟斤拷锟斤拷锟睫的ｏ拷锟斤拷锟斤拷远锟斤不锟斤拷2/3锟斤拷锟斤拷远小锟斤拷2/3锟斤拷锟斤拷锟斤拷片锟斤拷墓锟斤拷锟斤拷锟斤拷锟轿拷锟斤拷锟斤拷薜墓鄣锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷薅锟斤拷锟缴的★拷锟斤拷锟斤拷锟斤拷锟斤拷锟窖э拷系募锟斤拷薹锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷实0.666...锟斤拷2/3锟斤拷锟斤拷一锟斤拷写锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷一锟街憋拷锟斤方式锟斤拷锟斤拷么锟斤拷锟斤拷锟街わ拷锟�""0.666...=2/3""锟斤拷锟斤拷1锟斤拷2/3=0.6666锟斤拷锟斤拷循锟斤拷2/3=2/3锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷一锟斤拷锟斤拷锟街憋拷锟界：

锟斤拷锟斤拷锟斤拷锟斤拷锟杰伙拷锟斤拷锟斤拷锟斤拷锟剿感碉拷锟斤拷锟斤拷锟斤拷锟斤拷学锟叫ｏ拷锟斤拷锟斤拷知锟斤拷0.999锟斤拷锟斤拷一锟斤拷锟斤拷锟睫诧拷循锟斤拷锟斤拷小锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷思锟斤拷锟斤拷锟睫接斤拷锟斤拷1锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷1锟斤拷然锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷牵锟斤拷锟斤拷锟斤拷锟窖э拷系锟斤拷锟斤拷锟斤拷锟�0.999锟斤拷实锟斤拷锟较碉拷锟斤拷1锟斤拷

要锟斤拷锟斤拷为什么0.999锟斤拷锟斤拷锟斤拷1锟斤拷锟斤拷锟角匡拷锟斤拷通锟斤拷一些锟斤拷学锟斤拷锟斤拷锟斤拷锟斤拷锟叫斤拷锟酵★拷锟斤拷锟饺ｏ拷锟斤拷锟角匡拷锟皆斤拷0.999锟斤拷锟斤拷示为一锟斤拷锟斤拷锟筋级锟斤拷锟斤拷锟斤拷式锟斤拷

0.999锟斤拷 = 9/10 + 9/100 + 9/1000 + 锟斤拷

锟斤拷锟节ｏ拷锟斤拷锟角匡拷锟斤拷使锟矫硷拷锟斤拷锟斤拷偷墓锟绞斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟筋级锟斤拷锟侥和★拷

锟斤拷S = 9/10 + 9/100 + 9/1000 + 锟斤拷

锟斤拷么10S = 9 + 9/10 + 9/100 + 锟斤拷

锟斤拷锟角匡拷锟皆匡拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷墙锟�10S锟斤拷去S锟斤拷每一锟筋都锟结被锟斤拷去锟斤拷只锟斤拷锟斤拷9锟斤拷锟斤拷耍锟�

10S - S = 9

9S = 9

S = 1

锟斤拷锟皆ｏ拷锟斤拷锟斤拷锟斤拷学锟斤拷锟姐，锟斤拷锟角匡拷锟皆得筹拷锟斤拷锟桔ｏ拷0.999锟斤拷锟侥和碉拷锟斤拷1锟斤拷

锟斤拷一锟街凤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟绞癸拷眉锟斤拷薜母锟斤拷睢ｏ拷锟斤拷强锟斤拷越锟�0.999锟斤拷锟斤拷示为一锟斤拷锟斤拷锟睫ｏ拷

0.999锟斤拷 = lim(n锟斤拷锟斤拷) (9/10 + 9/100 + 9/1000 + 锟斤拷 + 9/10^n)

锟斤拷锟斤拷味锟脚碉拷n锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟绞憋拷锟�0.999锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟筋级锟斤拷锟侥和★拷然锟斤拷锟斤拷锟斤拷锟角匡拷锟斤拷证锟斤拷锟斤拷锟斤拷锟斤拷薜慕锟斤拷锟斤拷1锟斤拷

锟斤拷锟角匡拷锟斤拷使锟斤拷锟斤拷锟叫硷拷锟睫的讹拷锟斤拷锟斤拷证锟斤拷锟斤拷一锟姐。锟斤拷a_n = 0.999锟斤拷锟斤拷前n锟斤拷停锟�

a_1 = 0.9

a_2 = 0.99

a_3 = 0.999

...

a_n = 0.999锟斤拷 (n锟斤拷9)

锟斤拷锟角匡拷锟皆匡拷锟斤拷锟斤拷锟斤拷锟斤拷n锟斤拷锟斤拷锟接ｏ拷a_n锟金渐接斤拷1锟斤拷锟斤拷锟斤拷锟斤拷锟叫硷拷锟睫的讹拷锟藉，锟斤拷锟角匡拷锟皆得筹拷锟斤拷锟斤拷lim(n锟斤拷锟斤拷) a_n = 1锟斤拷

通锟斤拷锟斤拷锟斤拷锟街凤拷锟斤拷锟斤拷锟斤拷锟角匡拷锟斤拷确锟斤拷0.999锟斤拷锟斤拷锟斤拷1锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷劭锟斤拷芑锟斤拷锟斤拷烁械锟斤拷锟斤拷螅锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷嵌锟斤拷锟斤拷锟酵硷拷锟睫碉拷锟斤拷锟解不锟斤拷锟斤拷锟诫。锟斤拷学锟较碉拷锟斤拷锟斤拷锟酵讹拷锟斤拷确实锟斤拷锟斤拷0.999锟斤拷锟斤拷锟斤拷1锟斤拷

锟斤拷耍锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟窖э拷锟斤拷锟斤拷锟�0.999锟斤拷时锟斤拷锟斤拷锟角匡拷锟皆斤拷锟斤拷锟酵拷锟�1锟斤拷锟斤拷锟斤拷锟斤拷要锟斤拷锟斤拷锟斤拷锟斤拷之锟斤拷牟锟斤拷臁ｏ拷锟揭伙拷锟斤拷锟斤拷锟斤拷锟窖э拷涂锟窖э拷锟斤拷锟斤拷锟斤拷锟斤拷殴惴猴拷锟接︼拷茫锟斤拷锟斤拷锟斤拷诖锟斤拷锟斤拷锟斤拷锟酵硷拷锟睫碉拷锟斤拷锟斤拷隆锟�

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