Question

A=2+2 mũ 2+2 mũ 3+2 mũ 4 +...+2 mũ 100 chia hết cho 15

Answer 1

Lời giải:
$A=(2+2^2+2^3+2^4)+(2^5+2^6+2^7+2^8)+....+(2^{97}+2^{98}+2^{99}+2^{100})$

$=2(1+2+2^2+2^3)+2^5(1+2+2^2+2^3)+...+2^{97}(1+2+2^2+2^3)$

$=(1+2+2^2+2^3)(2+2^5+...+2^{97})$

$=15(2+2^5+...+2^{97})\vdots 15$

Ta có đpcm.