Question

S₁ = 1 + 2 + 2² + 2³ + ...... + 2⁶² + 2⁶³

 

S2=1 +3 + 3² + 3³+ .........+ 3²⁰

 

S₃ = 1 + 4 + 4² + 4³ + .........+44⁴³

 

GIÚP MÌNH VỚI NHA CÁC BẠN 

Answer 1

S₁ = \(1+2+2^2+2^3+...+2^{62}+2^{63}\)

2 . S₁ = \(2+2^2+2^3+2^4+...+2^{63}+2^{64}\)

2.S₁ - S₁ =\(\left(2+2^2+2^3+2^4+...+2^{63}+2^{64}\right)-\left(1+2+2^2+2^3+...+2^{62}+2^{63}\right)\)

S₁ = \(2^{64}-1\)

 

 

 

Answer 2

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

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

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

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

 

Answer 3

S₂ = \(1+3+3^2+3^3+...+3^{20}\)

3.S₂ = \(3+3^2+3^3+3^4+...+3^{21}\)

3.S₂ - S₂ = \(\left(3+3^2+3^3+3^4+...+3^{21}\right)-\left(1+3+3^2+3^3+...+3^{20}\right)\)

2.S₂ = \(3^{21}-1\)

S₂ = \(\left(3^{21}-1\right):2\)

Answer 4

\(S=1+3+3^2+3^3+...+3^{20}\)

\(3S=3+3^2 +3^3+3^4+...+3^{20}+3^{21}\)

\(3S-S=3^{21}-1\)

\(2S=3^{21}-1\)

\(S=\frac{3^{21}-1}{2}\)

Answer 5

S₃ = \(1+4+4^2+4^3+...+4^{43}\)

4.S₃ = \(4+4^2+4^3+4^4+...+4^{44}\)

4.S₃ - S₃ = \(\left(4+4^2+4^3+4^4+...+4^{44}\right)-\left(1+4+4^2+4^3+...+4^{43}\right)\)

3.S₃ = \(4^{44}-1\)

S₃ = \(\left(4^{44}-1\right):3\)