0.2+0.022+0.00222+...至无穷=______???

来源：百度知道 编辑：UC知道 时间：2024/05/31 05:47:38

解: 0.2+0.022+0.00222+…………….
=2/9(0.9+0.099+0.00999+…..)
=(2/9)[(1-0.1)+(0.1-0.001)+(0.01-0.00001)+….]
=(2/9)[(1+0.1+0.01+….)-(0.1+0.001+0.00001+….)]
=(2/9){[1/(1-0.1)]-[0.1/(1-0.01)]}…… Sn=a1/( 1- r)
=(2/9)(10/9-10/99)
=200/891
答: 200/891 Quelle:http://www.tonghuashun.cc/wiki/090203/408.html

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