Question

Cho

S=2⁰+2¹+2²+2³+2⁴+...+2¹⁰³

^{Chứng minh rằng :} 

^{a )} S chia hết cho 3

b ) S chia hết cho 15

c) S chia hết cho 255

Answer 1

\(S=\left(2^0+2^1\right)+\left(2^2+2^3\right)+...+\left(2^{102}+2^{103}\right)=3.2^0+3.2^2+.....+2^{102}.3=3.\left(2^0+2^2+....+2^{102}\right)\)

Vậy S chia hết chp 3 (đpcm)