Question

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

Answer 1

Ta có A = 2² + 2² + 2³ + 2⁴ + ............ + 2²⁰

=> 2A = 2.(2² + 2² + 2³ + 2⁴ + ............ + 2²⁰)

=> 2A = 2³ + 2³ + 2⁴ + 2⁵ + ............ + 2²¹ 

=> 2A - A = 2²¹ + 2³ - 2² - 2²

=> A = 2²¹ (đpcm)

Answer 2

Ta có A = 2² + 2² + 2³ + 2⁴ + ............ + 2²⁰

=> 2A = 2.(2² + 2² + 2³ + 2⁴ + ............ + 2²⁰)

=> 2A = 2³ + 2³ + 2⁴ + 2⁵ + ............ + 2²¹ 

=> 2A - A = 2²¹ + 2³ - 2² - 2²

=> A = 2²¹ (đpcm)

Answer 3

Ta có A = 2² + 2² + 2³ + 2⁴ + ............ + 2²⁰

=> 2A = 2.(2² + 2² + 2³ + 2⁴ + ............ + 2²⁰)

=> 2A = 2³ + 2³ + 2⁴ + 2⁵ + ............ + 2²¹ 

=> 2A - A = 2²¹ + 2³ - 2² - 2²

=> A = 2²¹ (đpcm)

Answer 4

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

\(\Rightarrow2A=2^3+2^3+2^4+...+2^{21}\)

\(\Rightarrow2A-A=\left(2^{21}+2^3\right)-\left(2^2+2^2\right)\)

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

\(=\left(2^{21}+8\right)-8\)

\(=2^{21}+8-8\)

\(=2^{21}\)