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Nhầm !!!!!

\(B-A=\frac{2012^{101}}{2011}-\frac{2012^{101}-1}{2011}=\frac{2012^{101}-\left(2012^{101}-1\right)}{2011}=\frac{1}{2011}\)

OK NHA

ai nhanh nhat dc 3 k nha

2012A = 2012(1 + 2012 + 2012² + .... + 2012¹⁰⁰)

= 2012 + 2012² + 2012³ + .... + 2012¹⁰¹

2012A - A = ( 2012 + 2012² + 2012³ + .... + 2012¹⁰¹) - (1 + 2012 + 2012² + .... + 2012¹⁰⁰)

2011A = 2012¹⁰¹ - 1

=> A = (2012¹⁰¹ - 1)/3

Vì (2012¹⁰¹ - 1)/2011 < 2012¹⁰¹/2011

=> A < B

Bạn kiểm tra lại đề nhé, hình như đề hơi có vấn đề

2A = 6+2^3+2^4+.....+2^2012

A = 2A - A = (6+2^3+2^4+.....+2^2012)-(3+2^2+2^3+......+2^2011)

                 = 6+2^2012 - 3 - 2^2

                 = 2^2012 - 1

=> A < B

Tk mk nha

ta có :

\(A=3+2^2+2^3+.....+2^{2011}.\)

\(\Rightarrow2A=6+2^3+2^4+....+2^{2012}\)

\(\Rightarrow A=\left(6+2^3+2^4+...+2^{2012}\right)-\left(3+2^2+2^3+....+2^{2011}\right)\)

\(\Rightarrow A=-1+2^{2012}\)

vì -1+2^2012<2^2012 nên A <B

Ta có:A=\(1+3+3^2+3^3+...+3^{2012}\)

      3A=\(3\cdot\left(1+3+3^2+3^3+...+3^{2012}\right)\)

      3A=\(3+3^2+3^3+3^4+...+3^{2013}\)

   3A-A=\(\left(3+3^2+3^3+3^4+...+3^{2013}\right)-\left(1+3+3^2+3^3+...+3^{2012}\right)\)

     2A=\(3+3^2+3^3+3^4+...+3^{2013}-1-3-3^2-3^3-...-3^{2012}\)

     2A=\(\left(3-3\right)+\left(3^2-3^2\right)+\left(3^3-3^3\right)+...+\left(3^{2012}-3^{2012}\right)+\left(3^{2013}-1\right)\)

    2A=\(0+0+0+...+0+3^{2013}-1\)

    2A=\(3^{2013}-1\)

     A=\(\frac{3^{2013}-1}{2}\)

    B=\(3^{2013}\div2\)

    B=\(\frac{3^{2013}}{2}\)

    VậyB-A=\(\frac{3^{2013}}{2}-\frac{3^{2013}-1}{2}\)

          \(B-A=\frac{3^{2013}-\left(3^{2013}-1\right)}{2}\)

          \(B-A=\frac{3^{2013}-3^{2013}+1}{2}\)

          \(B-A=\frac{1}{2}=0,5\)

\(\frac{3}{2}.A=\frac{3}{4}+\left(\frac{3}{2}\right)^2+\left(\frac{3}{2}\right)^3+...+\left(\frac{3}{2}\right)^{2013}\)

\(\Rightarrow\frac{3}{2}.A-A=\frac{3}{4}+\left(\frac{3}{2}\right)^2+\left(\frac{3}{2}\right)^3+...+\left(\frac{3}{2}\right)^{2013}-\left(\frac{1}{2}+\frac{3}{2}+\left(\frac{3}{2}\right)^2+...+\left(\frac{3}{2}\right)^{2012}\right)\)

\(\Rightarrow\frac{1}{2}.A=\frac{3}{4}+\left(\frac{3}{2}\right)^{2013}-\frac{1}{2}-\frac{3}{2}=\left(\frac{3}{2}\right)^{2013}-\frac{5}{4}\Rightarrow A=2.\left(\frac{3}{2}\right)^{2013}-\frac{5}{2}\)

\(B-A=\frac{1}{2}.\left(\frac{3}{2}\right)^{2013}-2.\left(\frac{3}{2}\right)^{2013}+\frac{5}{2}=-\left(\frac{3}{2}\right)^{2014}+\frac{5}{2}\)

Trần Thị Loan tại sao lại + 5/2?

ngu thế Bụng Mon

c1:A=B

c2:A=11

c3:B=1\20

c4:mk k bit

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