Question

Biết \(1^4+2^4+3^4....+10^4=25333\).

Tính nhanh: \(2^4+4^4+6^4+...+20^4\)

Answer 1

\(2^2+4^2+6^2+...+20^2\)

=\(\left(1.2\right)^4+\left(2.2\right)^4+\left(3.2\right)^4+...+\left(2.10\right)^4\)

=\(1^4.2^4+2^4.2^4+3^4.2^{\text{4}}+....+10^4.2^4\)

=\(2^4.\left(1^4+2^4+3^4+...+10^4\right)\)

=16.25333=405328