Question

C=5+5²+5³+...+5²⁰⁰⁴. Chứng minh C chia hết cho30 và 155

Answer 1

Ta có: C = 5 + 5² + 5³ + ...... + 5²⁰⁰⁴

=> C = (5 + 5²) + (5³ + 5⁴) + ...... + (5²⁰⁰³ + 5²⁰⁰⁴)

=> C = 1.30 + 5².(5 + 5²) + ...... + 5²⁰⁰².(5 + 25)

=> C = 1.30 + 5².30 + ...... + 5²⁰⁰².30

=> C = 30.(1 + 5² + ..... + 5²⁰⁰²) chia hết cho 30( đpcm)

Answer 2

Ta có: C = 5 + 5² + 5³ + ...... + 5²⁰⁰⁴

=> C = (5 + 5²) + (5³ + 5⁴) + ...... + (5²⁰⁰³ + 5²⁰⁰⁴)

=> C = 1.30 + 5².(5 + 5²) + ...... + 5²⁰⁰².(5 + 25)

=> C = 1.30 + 5².30 + ...... + 5²⁰⁰².30

=> C = 30.(1 + 5² + ..... + 5²⁰⁰²) chia hết cho 30( đpcm)

Answer 3

Ta có: C = 5 + 5² + 5³ + ...... + 5²⁰⁰⁴

=> C = (5 + 5²) + (5³ + 5⁴) + ...... + (5²⁰⁰³ + 5²⁰⁰⁴)

=> C = 1.30 + 5².(5 + 5²) + ...... + 5²⁰⁰².(5 + 25)

=> C = 1.30 + 5².30 + ...... + 5²⁰⁰².30

=> C = 30.(1 + 5² + ..... + 5²⁰⁰²) chia hết cho 30( đpcm)

Answer 4

C=5+5²+5³+...+5²⁰⁰⁴

C=(5+5²+5³)+...+(5²⁰⁰²+5²⁰⁰³+5²⁰⁰⁴)

C=5.(5+5²+5³)+...+5²⁰⁰².(5+5²+5³)

C=5.155+...+5²⁰⁰².155

C=155.(5+...+5²⁰⁰²) chia hết cho 155 (đpcm)