Question

Cho S=1+2+2^2+2^3+2^4+2^5+2^6+2^7+2^8+2^9. Hãy chứng minh S chia hết cho 3.

Answer 1

S=(1+2)+(2^2+2^3)+(2^4+2^5)+(2^6+2^7)+(2^8+2^9)

  =1.(1+2)+2^2.(1+2)+2^4.(1+2)+2^6.(1+2)+2^8.(1+2)

  =1.3+2^2.3+2^4.3+2^6.3+2^8.3

  =3.(1+2^2+2^4+2^6+2^8) chia hết cho 3

Answer 2

S=1+2+2^2+2^3+2^4+2^5+2^6+2^7

S= (1+2) + (2^2+2^3) + (2^4+2^5) + (2^6+2^7)

S=3 + 3.4 + 3.16 + 3.64

S=255

Vì 255 chia hết cho 3

=> S sẽ chia hết cho 3

Người lạ ơi bố thí cho tôi ^_^

Answer 3

 \(S\) = 1 + 2 + 2²+ 2³ + 2⁴ + 2⁵ + 2⁶ + 2⁷ + 2⁸ + 2⁹

\(\Rightarrow\)\(S\)= 2⁰ + 2¹ + 2²+ 2³ + 2⁴ + 2⁵ + 2⁶ + 2⁷ + 2⁸ + 2⁹
\(\Rightarrow\)\(S\)= ( 2⁰ + 2¹ ) + ( 2²+ 2³) + ( 2⁴ + 2⁵ ) + ( 2⁶ + 2⁷ ) + ( 2⁸ + 2⁹ )

\(\Rightarrow\) \(S\)= 2⁰ . ( 2⁰ + 2¹ ) + 2² . ( 2⁰ + 2¹ ) + 2⁴ . ( 2⁰ + 2¹ ) + 2⁶ . ( 2⁰ + 2¹ ) + 2⁸ . ( 2⁰ + 2¹ )

\(\Rightarrow\)\(S\)= 2⁰ . 3 + 2² . 3 + 2⁴ . 3 + 2⁶ . 3 + 2⁸ . 3

\(\Rightarrow\)\(S\)= 3 . ( 2⁰ + 2² + 2⁴ + 2⁶ + 2⁸ ) \(⋮\)3 ( đpcm )