Question

cho A=1+2+2 mũ 2+2 mũ 3+......+2 mũ 2019;

B= 2mũ 2020

tính : B-A

Answer 1

A = 1 + 2 + 2² + 2³ + ... + 2²⁰¹⁹

2A = 2(1 + 2 + 2² + ... + 2²⁰¹⁹)

2A = 2 + 2² + 2³ + ... + 2²⁰²⁰

=> 2A - A = (2 + 2² + 2³ + ... + 2²⁰²⁰) - (1 + 2 + 2² + .. +2²⁰¹⁹)

=> A = 2²⁰²⁰ - 1

B - A = 2²⁰²⁰ - (2²⁰²⁰ - 1) = 1

Answer 2

\(A=1+2+2^2+2^3+...+2^{2019}\)

\(2A=2\left(1+2+2^2+2^3+...+2^{2019}\right)\)

\(2A=2+2^2+2^3+2^4+...+2^{2020}\)

\(2A-A=\left(2+2^2+2^3+2^4+...+2^{2020}\right)-\left(1+2+2^2+2^3+...+2^{2019}\right)\)

\(A=2^{2020}-1\)

=> B - A =  \(2^{2020}-\left(2^{2020}-1\right)=\text{ấn máy tính đel ra :))))}\)

Answer 3

#)Giải :

\(A=1+2+2^2+2^3+...+2^{2019}\)

\(\Rightarrow2A=2+2^2+2^3+...+2^{2020}\)

\(\Rightarrow2A-A=\left(2+2^2+2^3+...+2^{2020}\right)-\left(1+2+2^2+2^3+...+2^{2019}\right)\)

\(\Rightarrow A=2^{2020}-1\)

\(\Rightarrow B-A=2^{2020}-\left(2^{2020}-1\right)\)

\(\Rightarrow B-A=2^{2020}-2^{2020}+1\)

\(\Rightarrow B-A=1\)

Vậy B - A = 1

Answer 4

\(A=1+2+2^2+2^3+...+2^{2019}\)

\(2A=2+2^2+2^3+2^4+...+2^{2020}\)

\(2A-A=\left(2+2^2+...+2^{2020}\right)-\left(1+2+...+2^{2019}\right)\)

\(A=2^{2020}-1\)

\(\Rightarrow B-A=2^{2020}-\left(2^{2020}-1\right)\)

\(B-A=2^{2020}-2^{2020}+1\)

\(B-A=1\)

Vậy ....

Answer 5

\(A=1+2+2^2+2^3+...+2^{2019}\)

\(2A=2+2^2+2^3+3^4+...+2^{2020}\)

\(2A-A=\left(2+2^2+2^3+...+2^{2020}\right)-\left(1+2+2^2+2^3+...+2^{2019}\right)\)

\(A=2^{2020}-1\)

\(B=2^{2020}\)

\(B-A=2^{2020}-\left(2^{2020}-1\right)\Leftrightarrow2^{2020}-2^{2020}+1=0+1=1\)

Chúc bạn học tốt !!!