Question

1+2+2²+2³+...+2⁶³=2⁶⁴-1

Answer 1

tính như nào nhỉ

 

Answer 2

`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`

Answer 3

Đặt \(A=1+2+2^2+2^3+...+2^{63}\)

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

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

Answer 4

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=2.22+23+....+2^63−1=2^3+2^3+...2^63−1=2.23+....+2^63−1=24+....+2^63−1=263.2−1=264−1

Answer 5

Đặt \(A=1+2+2^2+2^3+...+2^{63}\)

\(\Leftrightarrow2\cdot A=2+2^2+2^3+...+2^{64}\)

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