Question

Cho P = 1 + 2² + 2²+2⁴+2⁵+2⁶+2⁷ 

Chứng minh P chia hết cho 3 

Giusp mik luôn nha . Ai đúng mik sẽ tick cho

Answer 1

P = 1 +  ( 2² + 2³ ) + ( 2⁴ + 2⁵ ) + ( 2⁶ + 2⁷ )

P = 1 + 2 . ( 1 + 2 ) + 2 . ( 1 + 2 ) + 2 . ( 1 + 2 )

P = 1 + 2 . 3 + 2 . 3 + 2 . 3

Mỗi cặp đều có số 3 

=> P = 1 + 2² + 2³ + 2⁴ + 2⁵ + 2⁶ + 2⁷ chia hết cho 3

Answer 2

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

\(P=1+\left(2^2+2^3\right)+\left(2^4+2^5\right)+\left(2^6+2^7\right)\)

\(P=1+2^2\left(1+3\right)+2^4\left(1+2\right)+2^6\left(1+2\right)\)

\(P=1+2^2.3+2^4.3+2^6.3\)

\(P=\left(1+2^2+2^4+2^6\right).3⋮3\left(đpcm\right)\)