Question

Chứng minh rằng

a)S=3+3¹+3²+3³+3⁴+......+3²⁰

b)S=3+3²+3³+3⁴+........+3²⁰

chia hết cho 12

Answer 1

Phần a sai đề nha

b) S = 3 + 3² + 3³ + 3⁴ + ............ + 3²⁰

S = ( 3 + 3² ) + ( 3³ + 3⁴ ) + ........... + ( 3¹⁹ + 3²⁰ )

S = 3 . ( 1 + 3 ) + 3³ . ( 1 + 3 ) + ....... + 3¹⁹ . ( 1 + 3 )

S = 3 . 4 + 3³ . 4 + ............. + 3¹⁹ . 4

S = 12 + 27 . 4 + ........... + 3¹⁹ . 4

S = 12 + 108 + ........... + 3¹⁹ . 4

Mà 12 ; 108 \(⋮\) 12 \(\Rightarrow\) ( 12 + 108 + ............ + 3¹⁹ . 4 ) \(⋮\) 12

Vậy S \(⋮\) 12 ( ĐPCM )

Answer 2

b/S=3+3^2+3^3+3^4+......+3^20(gồm 21 số hạng)

S=(3+3^2)+(3^3+3^4)+(3^5+3^6)+......+(3^19+3^20)

S=1(3+3^2)+3^2(3+3^2)+......+3^18(3+3^2)

S=1.12 +3^2.12 +........+3^18.12

S=12.(1+3^2+3^4+......+3^18)

Vậy S chia hết cho 12

Answer 3

a

Answer 4

a

Answer 5

a

Answer 6

a

Answer 7

â

Answer 8

a

Answer 9

â

Answer 10

a

Answer 11

a

Answer 12

a

Answer 13

a

Answer 14

a

Answer 15

a

Answer 16

a

Answer 17

a