Question

Cho P=1+2+2^2+2^3+2^4+2^5+2^6+2^7 chứng minh P chia hết cho 3

Giúp tớ với nha 😊

Answer 1

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

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

P=1.(1+2)+\(2^2\)(1+2)+\(2^4\)(1+2)+\(2^6\)(1+2)

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

⇒P⋮3(đpcm)