Question

  a)Chứng minh rằng:7⁶+7⁵-7⁴ chia hết cho 55

  b)Tính :A=1+5+5²+53+.....5⁴⁹+5⁵⁰

Answer 1

7⁶+7⁵-7⁴

=7⁴.7²+7⁴.7-7⁴

=7⁴.(7²+7-1)=7⁴.55 chia hết cho 55

A=1+5+5²+......+5⁵⁰

=>5A=5+5²+5³+......+5⁵¹

=>5A-A=(5+5²+5³+.....+5⁵¹)-(1+5+5²+.....+5⁵⁰)

=>4A=5⁵¹-1

=>A=(5⁵¹-1)/4

Answer 2

b) 5A=5+5^2+5^3+...+5^50+5^51

5A-A=4A=5^51-1

Suy ra A=5^51-1/4