Question

b = 3 mũ 1 + 3 mũ 2 + 3 mũ 3 + 3 mũ 4 + 3 mũ 5 + chấm chấm chấm + 30 mũ 30 chứng minh Bchia hết cho13

Answer 1

B = 3¹ + 3² + 3³ + ... + 3²⁸ + 3²⁹ + 3³⁰

B = (  3¹ + 3² + 3³ ) + ... + ( 3²⁸ + 3²⁹ + 3³⁰ )

B = 3¹ . ( 1 + 3 + 3² ) + ... + 3²⁸ . ( 1 + 3 + 3² )

B = 3¹ . 13 + ... + 3²⁸ . 13

B = 13 . ( 3 + ... + 3²⁸ ) \(⋮\)13

Vậy B \(⋮\)13 ( dpcm )

Answer 2

\(B=3^1+3^2+3^3+3^4+3^5+............+3^{30}\)

\(\Rightarrow B=\left(3^1+3^2+3^3\right)+\left(3^4+3^5+3^6\right)+............+\left(3^{28}+3^{29}+3^{30}\right)\)

\(\Rightarrow B=3^1.\left(1+3+3^2\right)+3^4.\left(1+3+3^2\right)+.........+3^{28}.\left(1+3+3^2\right)\)

\(\Rightarrow B=3^1.13+3^4.13+.........+3^{28}.13\)

\(\Rightarrow B=13\left(3^1+3^4+.........+3^{28}\right)\)

Mà 13 \(⋮\)13 \(\Rightarrow13\left(3^1+3^4+...........+3^{28}\right)⋮13\)

Vậy B chia hết cho 13

Answer 3

đầu buồi

Answer 4

dung tục quá