Question

Cho B= 2+2^2+2^3+........+2^60

A) tính b               B) chứng minh B chia hết cho 3

Answer 1

\(B=2+2^2+2^3+...+2^{60}\)

\(2B=2^2+2^3+2^4+...+2^{61}\)

\(2B-B=\left(2^2+2^3+2^4+...+2^{61}\right)-\left(2+2^2+2^3+...+2^{60}\right)\)

\(B=2^{61}-2\)

\(B=2+2^2+2^3+...+2^{60}\)

\(=\left(2+2^2\right)+\left(2^3+2^4\right)+...+\left(2^{59}+2^{60}\right)\)

\(=2\left(1+2\right)+2^3\left(1+2\right)+...+2^{59}\left(1+2\right)\)

\(=3\left(2+2^3+...+2^{59}\right)⋮3\)