Question

Tính tổng sau:

S=1+2+2²+2³+..........................+2⁶²+2⁶³

Answer 1

Giải

S=1+2+2²+2³+....................+2⁶²+2⁶³

2S=2(1+2+2²+2³+.................+2⁶²+2⁶³)

2S=2+2²+2³+2⁴+............................+2⁶³+2⁶⁴)

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

S=2⁶⁴-1

Answer 2

Ta có:\(2^{64}-1=\left(2-1\right)\left(2^{63}+2^{62}+2^{61}+...+1\right)\)

Do đó S\(=2^{64}-1\)

Ngắn gọn quá phải không dùng hđt:\(a^n-b^n\)

Answer 3

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

Vậy \(S=2^{64}-1\).

Answer 4

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

\(2S=2+2^2+2^3+2^4+...+2^{63}+2^{64}\)

\(\Rightarrow2S-S=\left(2+2^2+2^3+2^4+...+2^{63}+2^{64}\right)-\left(1+2+2^2+2^3+...+2^{62}+2^{63}\right)\)

\(\Rightarrow S=2^{64}-1\)

Vậy \(S=2^{64}-1\).