Question

\(M=2^2+2^2+2^3+2^4+2^5+..........+2^{2019}+2^{2020}\) 

Ai nhanh nhất mình cho 1 👍nha!

Nhanh lên! mình cần gấp!!! 😭😭

Answer 1

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Answer 2

M = 2² + 2² + 2³  + 2⁴ + 2⁵  + ... + 2²⁰¹⁹ + 2²⁰²⁰

M - 2² = 2² + 2³ + 2⁴ + 2⁵ + ... + 2²⁰¹⁹ + 2²⁰²⁰

2M - 4 = 2(2² + 2³+ 2⁴ + 2⁵ + ... + 2²⁰¹⁹ + 2²⁰²⁰

2M - 4 = 2³ + 2⁴ + 2⁵ + 2⁶ + ... + 2²⁰²⁰ + 2²⁰²¹

2M - M - 4 = (2³ + 2⁴ + 2⁵ + 2⁶ + ... + 2²⁰²⁰ + 2²⁰²¹) - (2² + 2³ + 2⁴ + 2⁵ + ... + 2²⁰¹⁹ + 2²⁰²⁰)

M - 4 = 2²⁰²¹ - 2²

M = (2²⁰²¹ - 2²) + 4

M = 2²⁰²¹

Answer 3

<br class="Apple-interchange-newline"><div></div>2M= \(2^3+2^3+2^4+2^5+2^6+...+2^{2020}+2^{2021}\)

\(-\)

<br class="Apple-interchange-newline"><div></div>M=22+22+23+24+25+..........+22019+22020 

\(M=2^{2021}-\left(2^2+2^2\right)\)

Vậy \(M=2^{2021}-\left(2^2+2^2\right)\)