Question

tinh nhanh

 s = 1+2+2^2+2^3+2^4+....+2^9

Answer 1

Ta có :

\(S=1+2+...+2^9\)

\(\Rightarrow2S=2+2^2+....+2^{10}\)

\(\Rightarrow2S-S=\left(2+2^2+...+2^{10}\right)-\left(1+2+....+2^9\right)\)

\(\Rightarrow S=2^{10}-1\)

Answer 2

S = 1 + 2 + 2² + 2³ + 2⁴ + ... + 2⁹

2S = ( 1 + 2 + 2² + 2³ + 2⁴ + ... + 2⁹ ) . 2

2S = 2 + 2² + 2³ + 2⁴ + 2⁵ + ... + 2¹⁰

2S - S = ( 2 + 2² + 2³ + 2⁴ + 2⁵ + ... + 2¹⁰ ) - ( 1 + 2 + 2² + 2³ + 2⁴ + ... + 2⁹ )

S = 2¹⁰ - 1

S = 1024 - 1

S = 1023