Question

M 1 3 3 2 3 3 ... 3 98 3 99 3 100. chứng minh rằng M chia hết cho 13

Answer 1

M=1+3+3^2+3^3+...+3^98+3^99+3^100

M=(1+3+ 3^2)+(3^3+3^4+3^5)+...+(3^98+3^99+3^100)

M=(1+3+3^2)+3^3x(1+3+3^2)+...+3^98x(1+3+3^2)

M=13x3^3x13+...+3^98x13

=> 13x(1+3+3^3+...+3^98)chia hết cho 13

Vậy M chia hết cho 13

HT

Answer 2

*Sửa đề*

M = 1 + 3 + 3²  +....+ 3¹⁰⁰

M = ( 1 + 3 + 3²) + (3³ + 3⁴ + 3⁵) + ... + (3⁹⁸ + 3⁹⁹ + 3¹⁰⁰)

M = (1 + 3 + 3²) + 3³(1 + 3 + 3²) + .... + 3⁹⁸.(1 + 3 + 3²)

M = 13 . 1 + 13 . 3³+ ...... + 13 . 3⁹⁸

M = 13 . ( 1 + 3³ +....+ 3⁹⁸)

=> M chia hết cho 13