cm S = 1/3+1/3^2+…+1/3^2015 bé thua 1/2

Question

cm S = 1/3+1/3^2+…+1/3^2015 bé thua 1/2

in progress 0
Thiên Ân 5 years 2021-05-21T15:50:29+00:00 2 Answers 13 views 0

Answers ( )

  1. diemthu
    0
    2021-05-21T15:51:37+00:00
    Reply

    Ta có:

    `\qquad S = 1/3+1/{3^2}+…+1/{3^{2015}}`

    `=>3S=3.(1/ 3 +1/{3^2}+…+1/{3^{2015}})`

    `=>3S=1+1/ 3 +…+1/{3^{2014}}`

    `=>3S-S=(1+1/ 3 +…+ 1/{3^{2014}})-(1/ 3 +1/{3^2}+…+1/{3^{2015}})`

    `=>2S=1-1/{3^{2015}}`

    `=>S={1-1/{3^{2015}}}/2`

    `=>S=1/ 2 – {1/{3^{2015}}}/ 2`

    `=>S=1/ 2 -1/{2.3^{2015}}`

    Vì `1/{2.3^{2015}}>0`

    `=>S=1/ 2 -1/{2.3^{2015}}<1/ 2`

    Vậy `S=1/3+1/{3^2}+…+1/{3^{2015}}<1/ 2`

  2. Verity
    0
    2021-05-21T15:52:11+00:00
    Reply

    Đáp án:

     

    Giải thích các bước giải:

     

    cm-s-1-3-1-3-2-1-3-2015-be-thua-1-2

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )