Question

cho A=2+2^2+2^3+2^4+....+2^20

chứng tỏ rằng A chia hết cho 3 

Answer 1

A = ( 2 + 2^2 ) + ( 2^3 + 2^4 ) + ... + ( 2^19 + 2^20 )

A = 2( 1 + 2 ) + 2^3( 1 + 2 ) + ... + 2^19( 1 + 2 )

A = 3( 2 + 2^3 + ... + 2^19 )

=> A chia hết cho 3

Answer 2

A = 2+2²+2³+...+2²⁰ chia hết cho 3

A= (2+2²)+(2³+2⁴)+...+(2¹⁹+2²⁰)

A= 2(1+2)+2³(1+2)+...+2¹⁹(1+2)

A= 2.3+2³.3+...+2¹⁹.3

A= 3(2+2³+...+2¹⁹) chia hết cho 3

Vậy A chia hết cho 3

Answer 3

\(A=2+2^2+....+2^{20}.\)

\(A=\left(2+2^2\right)+....+\left(2^{19}+2^{20}\right)\)

\(A=2.\left(1+2\right)+....+2^{19}.\left(1+2\right)\)

\(A=2.3+....+2^{19}.3\)

\(A=3.\left(2+...+2^{19}\right)\)

\(\Rightarrow A⋮3\left(đpcm\right)\)