Question

Cho S=1+2+2²+2³+2⁴+..........+2⁶²+2⁶³. Tính S

Answer 1

S = 1 + 2 + 2² + 2³ + 2⁴ + ... + 2⁶² + 2⁶³

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

2S =  2 + 2² + 2³ + 2⁴ + 2⁵ + ... + 2⁶³ + 2⁶⁴

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

S = 2⁶⁴ - 1

Vậy S = 2⁶⁴ - 1

Answer 2

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

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

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

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

Answer 3

\(S=1+2+2^2+2^3+2^4+...+2^{62}+2^{63}\)\(2^{63}\)

 \(\Rightarrow2S=2+2^2+2^3+2^4+...+2^{62}+2^{63}+2^{64}\)

\(\Rightarrow2S-S=S=2^{64}-1\)

Vậy \(S=2^{64}-1\)