Question

Chứng minh rằng:

 S1=5+5^2+5^3+...+5^2004 chia hết cho 6;31;156

 

Answer 1

=> S1 = ( 5 + 5² ) + ( 5³ + 5⁴ ) + .... + ( 5²⁰⁰³ + 5²⁰⁰⁴ )

=> S1 = 5.( 1 + 5 ) + 5³.( 1 + 5 ) + .... + 5²⁰⁰³.( 1 + 5 )

=> S1 = 5.6 + 5³.6 + ....+ 5²⁰⁰³.6

=> S1 = 6.( 5 + 5³ + ... + 2²⁰⁰³ )

Vì 6 ⋮ 6 => S1 ⋮ 6 ( đpcm )

=> S1 = ( 5 + 5² + 5³ ) + ( 5⁴ + 5⁵ + 5⁶ ) + .... + ( 5²⁰⁰² + 5²⁰⁰³ + 5²⁰⁰⁴ )

=> S1 = 5.( 1 + 5 + 5² ) + 5⁴.( 1 + 5 + 5² ) + .... + 5²⁰⁰².( 1 + 5 + 5² )

=> S1 = 5.31 + 5⁴.31 + .... + 5²⁰⁰².31

=> S1 = 31.( 5 + 5⁴ + ... + 5²⁰⁰² )

Vì 31 ⋮ 31 => S1 ⋮ 31 ( đpcm )

=> S1 = ( 5 + 5² + 5³ + 5⁴ ) + ( 5⁵ + 5⁶ + 5⁷ + 5⁸ ) + ... + ( 5²⁰⁰¹ + 5²⁰⁰² + 5²⁰⁰³ + 5²⁰⁰⁴ )

=> S1 = 5.( 1 + 5 + 5.5 + 5³ ) + 5⁵.( 1 + 5 + 5.5 + 5³ ) + ... + 5²⁰⁰¹.( 1 + 5 + 5.5 + 5³ )

=> S1 = 5.156 + 5⁵ .156 + ... + 5²⁰⁰¹.156

=>S1 = 156.( 5 + 5⁵ + ... + 5²⁰⁰¹ )

Vì 156 ⋮ 156 nên S1 ⋮ 156 ( đpcm )

Answer 2

viet sai thi bai nay cung chi dang diem khong ma thoi nhin lai truoc khi bot