sum of n terms of series 0.3, 0.33, 0.333,-…

Question

sum of n terms of series 0.3, 0.33, 0.333,…….

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Khánh Gia 4 years 2021-08-09T12:28:01+00:00 2 Answers 20 views 0

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  1. Dau
    0
    2021-08-09T12:29:04+00:00
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    Answer:

    (9n+10)^(-n)-1)/27

    Step-by-step explanation:

    hope it helps

  2. minhkhoi
    0
    2021-08-09T12:29:46+00:00
    Reply

    9514 1404 393

    Answer:

      (9n +10^(-n) -1)/27

    Step-by-step explanation:

    The tricky part is figuring out how to describe the series. The general term can be described by …

      an = (1/3)(1 -10^(-n))

    Then the sum of n terms is …

      \displaystyle\sum_{k=1}^n{\frac{1-10^{-k}}{3}}=\frac{n}{3}-\frac{1-10^{-n}}{30(1-10^{-1})}=\boxed{\frac{9n+10^{-n}-1}{27}}

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