Question

 2 mũ 2 + 4 mũ 2 + 6 mũ 2 + ...... + 24 mũ 2

biết 1 mũ 2 + 2 mũ 2 + 3 mũ 2 + ...... + 12 mũ 2 = 625

Answer 1

Ta đặt : \(A=1^2+2^2+3^2+...+12^2=625\)

\(\Rightarrow2A=2^2+4^2+6^2+...+24^2\)

\(\Leftrightarrow2A=1250\)

Answer 2

Vì \(1^2+2^2+3^2+......+12^2=625\)

\(\Rightarrow2^2+4^2+6^2+.......+24^2\)

\(=\left(1.2\right)^2+\left(2.2\right)^2+\left(3.2\right)^2+........+\left(12.2\right)^2\)

\(=1^2.2^2+2^2.2^2+3^2.2^2+.....+12^2.2^2\)

\(=1^2.4+2^2.4+3^2.4+......+12^2.4\)

\(=4.\left(1^2+2^2+3^2+.......+12^2\right)\)

\(=4.625=2500\)

Answer 3

2² + 4² + 6² + ... + 24²

= ( 2.1 )² + ( 2.2 )² + ( 2.3 )² + ... + ( 2.12 )² 

= 2².1² + 2².2² + 2².3² + ... + 2².12²

= 2²( 1² + 2² + 3² + ... + 12² )

= 4.625 = 2500

Answer 4

\(2^2+4^2+6^2+...+24^2\)

\(=\left(2.1\right)^2+\left(2.2\right)^2+\left(2.3\right)^2+...+\left(2.12\right)^2\)

\(=2^2.1^2+2^2.2^2+2^2.3^2+...+2^2.12^2\)

\(=2^2\left(1^2+2^2+3^2+...+12^2\right)\)

\(=2^2.625=2500\)