Question

Chứng minh tổng A = 3 + 3² + 3³ + 3⁴ + 3⁵ + 3⁶ + 3⁷+ 3⁸ + 3⁹ ​​chia hết cho 13

Answer 1

\(A=3\left(1+3+3^2\right)+3^4\left(1+3+3^2\right)+3^7\left(1+3+3^2\right)\)

\(=\left(1+3+3^2\right)\left(3+3^4+3^7\right)=13\left(3+3^4+3^7\right)⋮13\) (đpcm)

Answer 2

Lời giải:

Ta có:

\(A=(3+3^2+3^3)+(3^4+3^5+3^6)+(3^7+3^8+3^9)\)

\(=(3.1+3.3+3.9)+(3^4.1+3^4.3+3^4.9)+(3^7.1+3^7.3+3^7.9)\)

\(=3.(1+3+9)+3^4\left(1+3+9\right)+3^7.\left(1+3+9\right)\)

\(=3.13+3^4.13+3^7.13\)

\(=13.(3+3^4+3^7)\) ⋮ 13 . Vậy: A ⋮ 13

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Answer 3

A = 3 + 3² + 3³ + 3⁴ + 3⁵ + 3⁶ + 3⁷ + 3⁸ + 3⁹

⇒ A = (3 + 3² + 3³) + (3⁴ + 3⁵ + 3⁶) + (3⁷ + 3⁸ + 3⁹)

⇒ A = 3(1 + 3 + 3²) + 3⁴(1 + 3 + 3²) + 3⁷(1 + 3 + 3²)

⇒ A = 3.13 + 3⁴.13 + 3⁷.13

⇒ A = 13(3 + 3⁴ + 3⁷) ⋮ 13

vậy A ⋮ 13