Question

A = 2 + 2^2 + 2^3 + 2^4 + ... + 2^100 chia hết cho 31

Các bn lm giúp mk vs nha !

Answer 1

Ta có:

\(A=2+2^2+2^3+2^4+....+2^{100}\)

\(=\left(2+2^2+2^3+2^4+2^5\right)+.....+\left(2^{96}+2^{97}+2^{98}+2^{99}+2^{100}\right)\)

\(=2\left(1+2+2^2+2^3+2^4\right)+....+2^{96}\left(1+2+2^2+2^3+2^4\right)\)

\(=2\times31+....+2^{96}\times31\)

\(=31\left(2+2^6+....+2^{96}\right)\)

\(\Rightarrow\)A chia hết cho 31 (vì có chứa thừa số 31)

Answer 2

 Nhưng 2 + 2^2 + 2^3 + 2^4 + 2^4 + 2^5 = 62 ko ra 31