Question

Biết rằng \(1^2+2^2+3^2+4^2+....+10^2=385\)

Tính tổng \(S=2^2+4^2+6^2+....+20^2\)

Answer 1

=1540

Answer 2

Bài làm

Ta thấy : \(2^2=4=4.1^2\)

\(4^2=16=4.2^2\)

\(6^2=36=4.3^2\)

.......

\(20^2=400=4.10^2\)

\(\Rightarrow S=2^2+4^2+6^2+....+20^2\)

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

         \(=4.385\)

         \(=1540\)

~ Hok Tốt ~

Answer 3

theo đầu bài ta có 

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

=\(\left(2\times1\right)^2+\left(2\times2\right)^2+\left(2\times3\right)^2+......+\left(2\times10\right)^2\)

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

=4\(\times\)385 

=1540