Question

Bài 2 

a) 12+ 2² + 3² + 4²+5²  và (1+2+3+4+5)²

b) 1³+ 2³+3^{3 +}4³ và (1+2+3+4)³

^c) 16 . 5²⁰⁰  và 5²⁰²

d) 18 . 4⁵⁰⁰ và 2¹⁰⁰⁴

e) 2022 . 2023 ²⁰²⁴ + 2023²⁰²⁴ và 2023²⁰²⁵

Answer 1

a: \(12+2^2+3^2+4^2+5^2\)

\(=12+4+9+16+25\)

\(=16+50=66\)

\(\left(1+2+3+4+5\right)^2=15^2=225\)

=>\(12+2^2+3^2+4^2+5^2< \left(1+2+3+4+5\right)^2\)

b: \(1^3+2^3+3^3+4^3=\left(1+2+3+4\right)^2< \left(1+2+3+4\right)^3\)

c: \(5^{202}=5^2\cdot5^{200}=25\cdot5^{200}>16\cdot5^{200}\)

d: \(18\cdot4^{500}=18\cdot2^{1000}\)

\(2^{1004}=2^4\cdot2^{1000}=16\cdot2^{1000}\)

=>\(18\cdot4^{500}>2^{1004}\)

e: \(2022\cdot2023^{2024}+2023^{2024}=2023^{2024}\left(2022+1\right)\)

\(=2023^{2025}\)