Question

cho A = 1+3+3 mũ 2+ 3 mũ 3+ ...+3 mũ 2026.Tìm số dư cho phép chia A cho 120

Answer 1

Lời giải:

$A=1+3+3^2+3^3+....+3^{2026}$

$=1+3+3^2+(3^3+3^4+3^5+3^6)+(3^7+3^8+3^9+3^{10})+....+(3^{2023}+3^{2024}+3^{2025}+3^{2026})$

$=13+3^2(3+3^2+3^3+3^4)+3^6(3+3^2+3^3+3^4)+...+3^{2022}(3+3^2+3^3+3^4)$

$=13+(3^2+3^6+...+3^{2022})(3+3^2+3^3+3^4)$

$=13+(3^2+3^6+...+3^{2022}).120$

$\Rightarrow A$ chia $120$ dư $13$