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

Toán Lớp 7: 2^ x-1 +2^ x-2 +2^ x-3 +…+2^ x-49 =2^ 49 -1 Ai giúp e

Home/ Toán Lớp 7: 2^ x-1 +2^ x-2 +2^ x-3 +…+2^ x-49 =2^ 49 -1 Ai giúp e

Toán Lớp 7: 2^ x-1 +2^ x-2 +2^ x-3 +…+2^ x-49 =2^ 49 -1 Ai giúp e

Tháng Bảy 3, 2022 Toán học 2 Comments 0 views

Toán Lớp 7: 2^ x-1 +2^ x-2 +2^ x-3 +…+2^ x-49 =2^ 49 -1
Ai giúp e

Comments ( 2 )

  1. tuyetanhthu
    tuyetanhthu
    3 Tháng Bảy, 2022 at 7:49 sáng
    Reply
    Giải đáp: 
    Lời giải và giải thích chi tiết:
    Đặt: \(A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+…+\frac{1}{2^{49}}\)
    => \(2A=1+\frac{1}{2}+\frac{1}{2^2}+…+\frac{1}{2^{48}}\)
    => \(2A-A=\left(1+\frac{1}{2}+\frac{1}{2^2}+…+\frac{1}{2^{48}}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^{49}}\right)\)
    => \(A=1-\frac{1}{2^{49}}=\frac{2^{49}-1}{2^{49}}\)
    \(2^{x-1}+2^{x-2}+2^{x-3}+…+2^{x-49}=2^{49}-1\)
    <=> \(\frac{2^x}{2}+\frac{2^x}{2^2}+\frac{2^x}{2^3}+…+\frac{2^x}{2^{49}}=2^{49}-1\)
    <=> \(2^x\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+…+\frac{1}{2^{49}}\right)=2^{49}-1\)
    <=> \(2^x.\frac{2^{49}-1}{2^{49}}=2^{49}-1\)
    <=> \(2^x=2^{49}\)
    <=> x = 49.

  2. baoquyen
    baoquyen
    3 Tháng Bảy, 2022 at 7:49 sáng
    Reply
    Ta có: 2^(x-1)+2^(x-2)+2^(x-3)+…+2^(x-49)=2^49 – 1
    Đặt X=2^(x-1)+2^(x-2)+2^(x-3)+…+2^(x-49)
    => 2X = 2^x + 2^(x-1)+2^(x-2)+…+2^(x-48)
    => 2X-X=(2^x + 2^(x-1)+2^(x-2)+…+2^(x-48))-(2^(x-1)+2^(x-2)+2^(x-3)+…+2^(x-49))
    =>X= 2^x-2^(x-49)
    X=2^x.1- 2^x.2^-49
    =>X= 2^x.(1-2^-49)
    =>X= 2^x.(1-1/(2^49))
    =>X= 2^x.((2^49-1)/(2^49))
    =>X= 2^x.((2^49-1)/(2^49))=2^49 – 1
    =>2^x=(2^49-1):((2^49-1)/(2^49))
    =>2^x=(2^49-1).((2^49)/(2^49-1))
    =>2^x=((2^49-1).2^49)/(2^49-1)
    =>2^x=2^49/1=2^49
    =>x=49
    #Chucbanhoctot
    #NguyenVanCuong2k9

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

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