Question

B=2 mũ 1 + 2 mũ 2 + 2 mũ 3 + .... +2 mũ 30 chứng minh rằng B chia hết cko 21

Answer 1

\(B=2+2^2+2^3+....+2^{30}\)

\(B=\left(2+2^2+2^3+2^4+2^5+2^6\right)+....+\left(2^{25}+2^{26}+2^{27}+2^{28}+2^{29}+2^{30}\right)\)

\(B=\left(2+2^2+2^3+2^4+2^5+2^6\right)+....+25^{24}\left(2+2^2+2^3+2^4+2^5+2^6\right)\)

\(B=126+...+2^{24}.126\)

\(B=126\left(1+...+2^{24}\right)\)

\(\Rightarrow B=126\left(1+...+2^{24}\right)⋮21\)

Vậy \(B⋮21\)

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