计算2/3+4/3^2+6/3^3+……+2000/3^1000

问题描述:

计算2/3+4/3^2+6/3^3+……+2000/3^1000
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S = 2/3+4/3^2+6/3^3+……+2000/3^1000
(1/3)S = 2/3^2+4/3^3+……+1998/3^1000+2000/3^1001
两式相减
(2/3)S=2/3+2/3^2+2/3^3+……+2/3^1000-2000/3^1001
=(2/3)【1-(1/3)^1000】/【1-(1/3)】-2000/3^1001
=1-(1/3)^1000-2000/3^1001
所以,S=【1-(1/3)^1000-2000÷3^1001】÷(2/3)