Question

Chứng minh

a,\(7^6+7^5-7^4:55\)

b,\(3^{n+3}+5^{n+3}+3^{n+1}+5^{n+2}⋮30,60\)

c,\(3+3^2+3^3+3^4+.....+3^{100}⋮120\)

d,\(81^7-27^9-9^{13}⋮405\)

Answer 1

a) \(7^6+7^5-7^4=7^4\left(7^2+7-1\right)=7^4.55⋮55\)

Answer 2

d) \(81^7-27^9-9^{13}\)

\(=\left(3^4\right)^7-\left(3^3\right)^9-\left(3^2\right)^{13}\)

\(=3^{28}-3^{27}-3^{26}\)

\(=3^{26}\left(3^2-3-1\right)=3^{226}.5=3^{222}.405⋮405\)

Answer 3

c) Nhóm 4 hạng tử lại sẽ ra vầy

\(120\left(1+3^5+...+3^{95}\right)⋮120\)

Answer 4

b) \(=3^n\left(3+27\right)+5^n\left(25+125\right)\)

\(=3^n.30+5^n.150=30\left(3^n+5^n.5\right)⋮30\)

Answer 5

lm kỹ hộ cái ko hiểu

Answer 6

Câu b là vầy :

( 3ⁿ⁺³ + 3ⁿ⁺¹ ) + ( 5ⁿ⁺³ + 5ⁿ⁺² )

= 3ⁿ. 3³ + 3ⁿ + 3 + 5ⁿ. 5³ + 5ⁿ. 5²

= 3ⁿ . ( 27 + 3 ) + 5ⁿ . (25 + 125)

....................................................