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222-9+11+12:2*14+14 = ? ( )

Toán Lớp 6: b,B=3+3²+3³+…+ $3^{2021}$ c,C=1-5+5²-5³+…- $5^{2021}$+$5^{2022}$ d,D=7-7²+7³-…+$7^{2013}$-$7^{2014}$

Tháng Tám 15, 2022 Toán học 2 Comments 0 views

Toán Lớp 6: b,B=3+3²+3³+…+ $3^{2021}$
c,C=1-5+5²-5³+…- $5^{2021}$+$5^{2022}$
d,D=7-7²+7³-…+$7^{2013}$-$7^{2014}$

Comments ( 2 )

  1. thanhtung
    thanhtung
    15 Tháng Tám, 2022 at 9:22 chiều
    Reply
    b ) B = 3 + 3^2 + 3^3 + … + 3^2021
    => 3B = 3^2 + 3^3 + 3^4 + … + 3^2022
    => 3B – B = ( 3^2 + 3^3 + 3^4 + … + 3^2022 ) – (3 + 3^2 + 3^3 + … + 3^2021)
    => 2B = 3^2022 – 3
    => B = {3^2022 – 3}/2
    Vậy B = {3^2022 – 3}/2
    c ) C = 1 – 5 + 5^2 – 5^3 + … – 5^2021 + 5^2022
    => C = 5^2022 – 5^2021 + 5^2020 – … + 5 – 1
    => 5C = 5^2023 – 5^2022 + 5^2021 – … + 5^2 – 5
    => 5C – C = (5^2023 – 5^2022 + 5^2021 – … + 5^2 – 5 ) – ( 1 – 5 + 5^2 – 5^3 + … – 5^2021 + 5^2022 )
    => 4C = 5^2023 – 1
    => C = {5^2023 – 1}/4
    Vậy C = {5^2023 – 1}/4
    d ) D = 7 – 7^2 + 7^3 – … + 7^2013 – 7^2014
    => D = 7^2014 + 7^2013 – 7^2012 + … – 7^2 + 7
    => 7D = 7^2015 + 7^2014 – 7^2013 + … – 7^3 + 7^2
    => 7D – D = ( 7^2015 + 7^2014 – 7^2013 + … – 7^3 + 7^2 ) – ( 7^2014 + 7^2013 – 7^2012 + … – 7^2 + 7 )
    => 6D = 7^2015 – 7
    => D = {7^2015 – 7}/6
    Vậy D = {7^2015 – 7}/6
    #dtkc

  2. lantrungbach
    lantrungbach
    15 Tháng Tám, 2022 at 9:22 chiều
    Reply
    b)B=3+3^2+3^3+……………+3^2021
    3B=3^2+3^3+3^4+……………….+3^2022
    3B-B=(3^2+3^3+3^4+……………….+3^2022)-(3+3^2+3^3+……………+3^2021)
    2B=3^2022-3
    B=(3^2022-3)/2
    Vậy B=(3^2022-3)/2
    c)C=1-5+5^2-5^3+……………..-5^2021+5^2022
    C=5^2022 – 5^2021 + 5^2020 -……………..+ 5 – 1
    5C=5^2023-5^2022+5^2021-………………+5^2-5
    5C-C=(5^2023-5^2022+5^2021-………………+5^2-5)-(5^2022 – 5^2021 + 5^2020 -……………..+ 5 – 1)
    4C=5^2023-1
    C=(5^2023-1)/4
    Vậy C=(5^2023-1)/4
    d)D=7-7^2+7^3-…………….+7^2013-7^2014
    D=7^2014 + 7^2013 – 7^2012 +……………- 7^2 + 7
    7D=7^2015+7^2014-7^2013+……………..-7^3+7
    7D-D=(7^2015+7^2014-7^2013+……………..-7^3+7)-(7^2014 + 7^2013 – 7^2012 +……………- 7^2 + 7)
    6D=7^2015-7
    D=(7^2015-7)/6
    Vậy D=(7^2015-7)/6
     

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222-9+11+12:2*14+14 = ? ( )

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