Question

A = 1 +2+2^2 +2^3+...+2^99 chia hết cho 3

b=1+2+2^2+2^3+..+2^100 chia 3 dư 1

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Answer 1

\(\Rightarrow A=\left(1+2\right)+\left(2^2+2^3\right)+......+\left(2^{98}+2^{99}\right)\)

\(\Rightarrow A=\left(1+2\right)+2^2\left(1+2\right)+...+2^{98}\left(1+2\right)\)

\(\Rightarrow A=3+2^2.3+....+2^{98}.3\)

\(\Rightarrow A=3\left(1+2^2+....+2^{98}\right)\)

\(Vì3⋮3_{_{ }}\)\(\Rightarrow3\left(1+2^2+...+2^{98}\right)⋮3\)

Vậy Achia hết cho 3