Question

cho s= 2^{1 +}  2 ²+ 2³+...+2 ¹⁰⁰

chung to rang 

s:3

s :5

Answer 1

 s= 2^{1 +}  2 ²+ 2³+...+2 ¹⁰⁰

S = (2^1 + 2^2 + 2^3 + 2^4) + ...+ ( 2^97+2^98+2^99+2^100) 

S= 2( 1+ 2+ 2^2 + 2^3) +...+ 2^97( 1+ 2 + 2^2 + 2^3)

S= 2. 15 +... + 2^97 . 15

S= 15( 2+ 2^5+.... + 2^97)

S= 5.3( 2+ 2^5+.... + 2^97))

=> S chia hết cho 3 và chia hết cho 5

Answer 2

s= 2^{1 +}  2 ²+ 2³+...+2 ¹⁰⁰ 

S = (2^1+2^2) + (2^3 + 2^4)+.....+ (2^99 + 2^100)

S = 2(1+2) + 2^3( 1 + 2)+....+2^99( 1+2)

S= 2.3 + 2^3.3 + ...+ 2^99. 3

S = 3( 2+2^3 +...+ 2^99) 

=> S chia hết cho 3