Question

chung to rang :1+ 5+ 5² + ...+ 5⁴⁰⁴ chia het cho 31

Answer 1

1+5+5²+....+5⁴⁰⁴

= (1+5+5²) + (5³+5⁴+5⁵) + .......+ (5⁴⁰² + 5⁴⁰³ + 5⁴⁰⁴)

= 1(1+5+5²) + 5³(1+5+5²) +......+ 5⁴⁰²(1+5+5²)

= 1. 31 + 5³. 31 +......+5⁴⁰². 31

= 31(1 + 5³ + ......... + 5⁴⁰²) chia hết cho 31 (đpcm)

Answer 2

1+5+5²+....+5⁴⁰⁴

= (1+5+5²) + (5³+5⁴+5⁵) + .......+ (5⁴⁰² + 5⁴⁰³ + 5⁴⁰⁴)

= 1(1+5+5²) + 5³(1+5+5²) +......+ 5⁴⁰²(1+5+5²)

= 1. 31 + 5³. 31 +......+5⁴⁰². 31

= 31(1 + 5³ + ......... + 5⁴⁰²) chia hết cho 31 (đpcm)