Chứng minh: A=1/1×3 + 1/3×5 + …. +1/(2n-1)(2n+1) <1/2

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Chứng minh: A=1/1×3 + 1/3×5 + …. +1/(2n-1)(2n+1) <1/2

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Maria 4 tuần 2021-08-15T23:00:19+00:00 1 Answers 4 views 0

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    2021-08-15T23:02:17+00:00

    Giải thích các bước giải: ta có

    $$\frac{1}{{1*3}} + \frac{1}{{3*5}} + \frac{1}{{5*7}}… + \frac{1}{{(2n – 1)(2n + 1)}} = \frac{1}{2} – \frac{1}{6} + \frac{1}{6} – \frac{1}{{10}} + \frac{1}{{10}} – \frac{1}{{14}}… + \frac{1}{{2(2n – 1)}} – \frac{1}{{2(2n + 1)}} = \frac{1}{2} – \frac{1}{{2(2n + 1)}}$$ < $\frac{1}{2}$ 

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