Question

1, cho biểu thức A = 1 + 2^{1 +} 2^{2 +} 2³ + ... + 2²⁰¹⁸

chứng minh A = 2²⁰¹⁸ - 11

2,cho biểu thức B = 1 + 3¹ + 3² + 3³ + .... + 3²⁰¹⁸

chứng minh B = (3^{2019 -} 1) : 2

3, cho biểu thức C = 1 + 4¹ + 4² + 4³  + ... + 4²⁰¹⁸

chứng minh C = ( 4^{2019 -} 1) : 3

Answer 1

\(A=1+2^1+2^2+...+2^{2017}\)

\(2A=2+2^2+2^3+...+2^{2018}\)

\(2A-A=2^{2018}-1hayA=2^{2018}-1\)

2; 3 tuong tu

Answer 2

1) A = 1 + 2 + 2² + 2³ + .... + 2²⁰¹⁸

2A = 2 + 2² + 2³ + 2⁴ + ..... + 2²⁰¹⁹

2A - A = ( 2 + 2² + 2³ + 2⁴ + ..... + 2²⁰¹⁹ ) - ( 1 + 2 + 2² + 2³ + .... + 2²⁰¹⁸ )

Vậy A = 2²⁰¹⁹ - 1

2) B = 1 + 3 + 3² + 3³ + ..... + 3²⁰¹⁸

3A = 3 + 3² + 3³ + ...... + 3²⁰¹⁹

3A - A = ( 3 + 3² + 3³ + ...... + 3²⁰¹⁹ ) - ( 1 + 3 + 3² + 3³ + ..... + 3²⁰¹⁸ )

2A = 3²⁰¹⁹ - 1

Vậy A = ( 3²⁰¹⁹ - 1 ) : 2

3) C = 1 + 4 + 4² + 4³ + ...... + 4²⁰¹⁸

4A = 4 + 4² + 4³ + ...... + 42019

4A - A = ( 4 + 4² + 4³ + ...... + 4²⁰¹⁹ ) - ( 1 + 4 + 4² + 4³ + ...... + 4²⁰¹⁸ )

3A = 4²⁰¹⁹ - 1

Vậy A = ( 4²⁰¹⁹ - 1 ) : 3

Answer 3

\(A=1+2+2^2+2^3+....+2^{2018}\)

\(2A=2+2^2+2^3+....+2^{2019}\)

\(A=2^{2019}-1\)

\(B=1+3+3^2+....+3^{2018}\)

\(3B=3+3^2+3^3+....+3^{2019}\)

\(2B=3^{2019}-1\)

\(B=\frac{2^{2019}-1}{2}\)

\(C=1+4+4^2+...+4^{2018}\)

\(\Rightarrow4B=4+4^2+4^3+...+4^{2019}\)

\(\Rightarrow3B=4^{2019}-1\)

\(\Rightarrow B=\frac{4^{2019}-1}{3}\)