Question

chứa tỏ chia hết cho 31 

2+2 mũ 2 + 2 mũ 4+.. +2 mũ 10

mình cần gấp lắm

Answer 1

Ta có: \(2+2^2+2^3+2^4+...+2^{10}\)

\(=\left(2+2^2+2^3+2^4+2^5\right)+\left(2^6+2^7+2^8+2^9+2^{10}\right)\)

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

\(=2\cdot31+2^6\cdot31\)

\(=31\cdot\left(2+2^6\right)⋮31\)