Question

B=3³+3⁴+.....+3⁶¹+3⁶²

Tìm số dư khi chia B cho 13

Answer 1

\(B=3^3+3^4+................+3^{61}+3^{62}\)(60 số hạng)

\(\Rightarrow B=\left(3^3+3^4+3^5\right)+\left(3^6+3^7+3^8\right)+...................+\left(3^{60}+3^{61}+3^{62}\right)\)

(20 nhóm)

\(\Rightarrow B=3^3\left(1+3+3^2\right)+3^6\left(1+3+3^2\right)+...........+3^{60}\left(1+3+3^2\right)\)

\(\Rightarrow B=3^3.13+3^6.13+.............+3^{60}.13\)

\(\Rightarrow B=13\left(3^3+3^6+.....+3^{60}\right)⋮13\)

\(\Rightarrow\) Số dư khi B chia cho 13 là 0

Answer 2

Ta có

B = 3³ + 3⁴ + 3⁵ + 3⁶ + ... + 3⁶¹+ 3⁶² (60 số hạng)

B = (3³ + 3⁴ + 3⁵) + ... + (3⁶⁰ + 3⁶¹ + 3⁶²) (20 nhóm)

B = 3³(1 + 3 + 3²) + ... + 3⁶⁰(1 + 3 + 3²)

B = 3³.13 + 3⁶.13 + ... + 3⁶⁰.13

B = 13(3³ + 3⁶ + ...+ 3⁶⁰) \(⋮\)13

=> B chia cho 3 dư 0