Question

viết tổng A=2^2+2^2+2^3+2^4+....+2^20 dưới dạng lũy thừa của 2

 

Answer 1

\(A=2+2^2+...+2^{20}\)

\(2A=2^2+2^3+...+2^{21}\)

\(A=2^{21}-2\)

Answer 2

\(A=4+2^2+2^3+.......+2^{20}\)

\(A=4+2^2+2^3+.......+2^{20}\)

\(2A=8+2^{3^{ }}+.........+2^{21}\)

\(2A-A=A=2^{21}+2^{20}+......+8-4-2^2-......-2^{20}\)

\(A=2^{21}\)

Answer 3

M=22+22+23+24+25+......+21975Taco:2M=23+23+24+25+26+......+219762M−M=(21976+23)−(22+22)M=(21976+23)−(4+4)=(21976+23)−8=21976+8−8=21976

Answer 4

\(A=2^2+2^2+2^3+2^4+....+2^{20}\)

\(A-2^2=2^2+2^3+2^4+.....+2^{20}\)

\(2\left(A-2^2\right)=2^3+2^4+2^5+....+2^{21}\)

\(2\left(A-2^2\right)-\left(A-2^2\right)=\left(2^3+2^4+2^5+...+2^{21}\right)-\left(2^2+2^3+2^4+...+2^{20}\right)\)

\(A-2^2=2^{21}-2^2\)

\(\Rightarrow A=2^{21}\)

Answer 5

A = 4+2^2+2^3+2^4+...+2^20

=>2A = 8+2^3+2^4+2^5+...+2^20+2^21

=>2A - A = A = 8+2^3+2^4+2^5+...+2^20+2^21-(4+2^2+2^3+2^4+...+2^20)

=>A = 8+2^3+2^4+2^5+...+2^20+2^21-8-2^3-2^4-...-2^20

=>A = 2^21

Answer 6

A = 2^2+2^2+2^3+2^4+.......+2^20

2A = 8+2^3+2^4+2^5+.........+2^21

2A - A = A = (8+2^3+2^4+2^5+.......+2^21)-(2^2+2^2+2^3+2^4+...+2^20)

A = 8+2^3+2^4+2^5+......+2^21-8+2^3+2^4+.......+2^20

=> A = 2^21

Answer 7

2A=8+2^3+2^4+2^5+...+2^21

2A-A=A=(8+2^3+2^4+2^5+...+2^21)-(2^2+2^2+2^3+2^4+...+2^20)

A=8+2^3+2^4+2^5+...+2^21-8-2^3-2^4-...-2^20

A=2^21