Đáp án:
Giải thích các bước giải:
`P=(1-1/2).(1-1/3).....(1-1/9)`
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`P=1/2 . 2/3 ..... 8/9`
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`P=\frac{1.2....8}{2.3....9}`
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`P=1/9`
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$\dfrac{1}{100}+\dfrac{1}{101}+...+\dfrac{1}{300}$
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Ta có: $\dfrac{1}{100}>\dfrac{1}{300}$ $;$ $\dfrac{1}{101}>\dfrac{1}{300}$ $;...;$ $\dfrac{1}{300}=\dfrac{1}{300}$
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$⇒\dfrac{1}{100}+\dfrac{1}{101}+...+\dfrac{1}{300}>\dfrac{1}{300}+\dfrac{1}{300}+...+\dfrac{1}{300}$
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$⇒\dfrac{1}{100}+\dfrac{1}{101}+...+\dfrac{1}{300}>\dfrac{200}{300}$
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$⇒\dfrac{1}{100}+\dfrac{1}{101}+...+\dfrac{1}{300}>\dfrac{2}{3}$ (đpcm)
