Question

S=2mũ1+2mũ2+2mũ3+....+2mũ60. Chứng tỏ S chia hết cho 3

Answer 1

S = ( 2¹ + 2² ) + ( 2³ + 2⁴ ) + ..... + ( 2⁵⁹ + 2⁶⁰ )

S = 2 x ( 1 + 2 ) + 2³ x ( 1 + 2 ) + .......... + 2⁵⁹ x ( 1 + 2 )

S = 2 x 3 + 2³ x 3 + ..... + 2⁵⁹ x 3

S = ( 2 + 2³ + ........ + 2⁵⁹ ) x 3

mà 3 \(⋮\)3 => S \(⋮\) 3

Answer 2

Ta có :

S= 2^1+2^2+2^3+...+2^60

S= (2^1+2^2)+(2^3+2^4)+...+(2^59+2^60)

s=2(1+2)+2^3(1+2)+...+2^59(1+1)

S= 3(2+2^3+...+2^59)

=> đpcm

Answer 3

S = 2 + 2^2 + 2^3 + ..... + 2^60

=> 2S = 2^2 + 2^3 + 2^4 + ..... + 2^61

=> 2S - S = 2^61 - 2

=> s = 2^61 - 2