Question

[Hằng Phạm]

CMR : 2⁰ + 2¹ + .... + 2⁹ + .... + 2^5n-5 + .... + 2^5n-1 chia hết cho 31 
Ai làm thì làm nhé !

Answer 1

[Minh Hiền]

Đặt \(A=\left(1+2+2^2+2^3+2^4\right)+\left(2^5+2^6+2^7+2^8+2^9\right)+...+\left(2^{5n-5}+2^{5n-4}+2^{5n-3}+2^{5n-2}+2^{5n-1}\right)\)

\(=\left(1+2+4+8+16\right)+2^5.\left(1+2+4+8+16\right)+...+2^{5n-5}.\left(1+2+4+8+16\right)\)

\(=31+2^5.31+...+2^{5n-5}.31\)

\(=31.\left(1+2^5+...+2^{5n-5}\right)\text{ chia hết cho 31}\)

=> A chia hết cho 31 (đpcm).