Question

Bài 5. Cho B = 3⁰ + 3¹ + 3² + 3³ + .... + 3¹⁰⁰. Chứng tỏ B chia hết cho 13

Answer 1

\(B=3^0+3^1+3^2...+3^{100}\)

\(=3^0\times\left(1+3^1+3^2\right)+3^3\times\left(1+3^1+3^2\right)+...+3^{98}\times\left(1+3^1+3^2\right)\)

\(=3^0\times13+3^3\times13+...+3^{98}\times13\)

\(=13\times\left(3^0+3^3+...+3^{98}\right)⋮13\)

Answer 2

B=30+31+32...+3100B=30+31+32...+3100

=30×(1+31+32)+33×(1+31+32)+...+398×(1+31+32)=30×(1+31+32)+33×(1+31+32)+...+398×(1+31+32)

=30×13+33×13+...+398×13=30×13+33×13+...+398×13

=13×(30+33+...+3