Question

[Vũ Trâm Anh]

1.So sánh

A = 1 + 5 ² + 5 ⁴ + ...+ 5 với 5 ^{42 -} 2 / 24

2.So sánh

1 + 7 ² + 7 ⁴+ ... +7 ⁶ +...+7 ¹⁰⁰  với 7¹⁰² -2019 / 2021

3. CMR (chứng minh rằng) 1 + 5² + 5⁴ +...+ 5²⁶ chia hết cho 26

4. CMR (chứng minh rằng) 1+2²+2⁴+...+2¹⁰⁰  chia hết cho 21

5.CMR (chứng minh rằng) 1+3²+3⁴+3⁶+...+3¹⁰⁰ chia hết cho 82

Answer 1

[༺༒༻²ᵏ⁸]

\(3,1+5^2+5^4+...+5^{26}\)

\(=\left(1+5^2\right)+\left(5^4+5^6\right)+...+\left(5^{24}+5^{26}\right)\)

\(=\left(1+5^2\right)+5^4\left(1+5^2\right)+...+5^{24}\left(1+5^2\right)\)

\(=26+5^4.26+...+5^{24}.26\)

\(=26\left(5^4+...+5^{24}\right)\)

Vì  \(26⋮26\)

\(\Rightarrow26\left(5^4+...+5^{24}\right)⋮26\)

\(\Rightarrow1+5^2+5^4+...+5^{26}⋮26\)

Answer 2

[༺༒༻²ᵏ⁸]

\(4,1+2^2+2^4+...+2^{100}\)

\(=\left(1+2^2+2^4\right)+...+\left(2^{98}+2^{99}+2^{100}\right)\)

\(=\left(1+2^2+2^4\right)+....+2^{98}\left(1+2^2+2^4\right)\)

\(=21+2^6.21...+2^{98}.21\)

\(=21\left(2^6+...+2^{98}\right)\)

Có : \(21\left(2^6+...+2^{98}\right)⋮21\)

\(\Rightarrow1+2^2+2^4+...+2^{100}⋮21\)