1﹢1/3﹢1/3²﹢1/3³﹢.﹢1/3²º¹¹等于多少?
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![1﹢1/3﹢1/3²﹢1/3³﹢.﹢1/3²º¹¹等于多少?](/uploads/image/z/1786449-57-9.jpg?t=1%EF%B9%A21%EF%BC%8F3%EF%B9%A21%EF%BC%8F3%26%23178%3B%EF%B9%A21%EF%BC%8F3%26%23179%3B%EF%B9%A2.%EF%B9%A21%EF%BC%8F3%26%23178%3B%26%23186%3B%26%23185%3B%26%23185%3B%E7%AD%89%E4%BA%8E%E5%A4%9A%E5%B0%91%3F)
1﹢1/3﹢1/3²﹢1/3³﹢.﹢1/3²º¹¹等于多少?
1﹢1/3﹢1/3²﹢1/3³﹢.﹢1/3²º¹¹等于多少?
1﹢1/3﹢1/3²﹢1/3³﹢.﹢1/3²º¹¹等于多少?
设S=1﹢1/3﹢1/3²﹢1/3³﹢.﹢1/3²º¹¹
两边乘以3得
3S=3﹢1﹢1/3﹢1/3²﹢.﹢1/3……1/3^2010
想减得:2S=3-1/3²º¹¹
∴1﹢1/3﹢1/3²﹢1/3³﹢.﹢1/3²º¹¹
=3/2-1/﹙2×3²º¹¹﹚
等比数列求和
[1 - 1/3²º¹²] / (1-1/3) = (1/2) * [ 3 - 1 / 3²º¹¹]