A=1+2+2²+2³+...+2⁶²+2⁶³

2A=2+2²+2³+2⁴+...+2⁶³+2⁶⁴

2A-A=2+2²+2³+2⁴+...+2⁶³+2⁶⁴-1+2+2²+2³+...+2⁶²+2⁶³

A=2⁶⁴-1

\(A=1+2+2^2+2^3+..+2^{62}+2^{63}\)

\(2A=2+2^2+2^3+...+2^{63}+2^{64}\)

\(2A-A=2^{64}-1\)

\(A=2^{64}-1\)

A=1+2+2²+2³+...+2⁶²+2⁶³

2A=2(1+2+2²+2³+...+2⁶²+2⁶³)

2A=2+2³+2⁴+2⁵...+2⁶³+2⁶⁴

2A-A=(2+2³+2⁴+2⁵...+2⁶³+2⁶⁴)-(1+2+2²+2³+...+2⁶²+2⁶³)

A=2⁶⁴-1

Nha bạn. Chúc bn ht

A = 1 + 2 + 2² + 2³ + ... + 2⁶² + 2⁶³

2A = 2 + 2² + 2³ + 2⁴ + ... + 2⁶³ + 2⁶⁴

A = 2⁶⁴ - 1

\(S_1=1+2+2^2+2^3+..+2^{63}\\ \Rightarrow2S_1=2+2^2+2^3+2^4+...+2^{64}\\ \Rightarrow S_1-2S_1=1-2^{64}\\ \Rightarrow-S_1=1-2^{64}\\ \Rightarrow S_1=2^{64}-1.\)

- Ta có: S₁ = 1 + 2 + 2² + 2³ + … + 2⁶³ = 1 + 2(1 + 2 + 2² + 2³ + … + 2⁶²) (1)

= 1 + 2(S₁ - 2⁶³) = 1 + 2S₁ - 2⁶⁴ S₁ = 2⁶⁴ - 1

H2.right

`#3107.101107`

`S_1 = 1 + 2 + 2^2 + 2^3 + ... + 2^63`

`2S_1 = 2 + 2^2 + 2^3 + .... + 2^64`

`2S_1 - S_1 = (2 + 2^2 + 2^3 + ... + 2^64) - (1 + 2 + 2^2 + 2^3 + ... + 2^63)`

`S_1 = 2 + 2^2 + 2^3 + ... + 2^64 - 1 - 2 - 2^2 - 2^3 - ... - 2^63`

`S_1 = 2^64 - 1`

Vậy, `S_1 = 2^64 - 1.`

tính như nào nhỉ

`1+2+2^2+2^3+....+2^63`

`=2+2+2^2+2^3+....+2^63-1`

`=2.2+2^2+2^3+....+2^63-1`

`=2^2+2^2+2^3+....+2^63-1`

`=2.2^2+2^3+....+2^63-1`

`=2^3+2^3+...2^63-1`

`=2.2^3+....+2^63-1`

`=2^4+....+2^63-1`

`=2^{63}.2-1=2^64-1`

Đặt \(A=1+2+2^2+2^3+...+2^{63}\)

\(\Rightarrow2A=2+2^2+2^3+2^4+2^5+...+2^{64}\)

\(\Rightarrow A=2A-A=\left(2+2^2+2^3+2^4+...+2^{64}\right)-\left(1+2+2^2+2^3+...+2^{63}\right)=2^{64}-1\left(đpcm\right)\)

\(=526+1590-262+795=2649\)

\(=265\cdot\left(3+2\cdot3\right)-263\cdot3-262=1334\)

= 1334