Ta có:

\(2^2\left(1^2+2^2+3^2+...+10^2\right)=2^2+4^2+6^2+...+20^2=S\)

=> \(S=2^2.385=1540\)

S=2^2+4^2+6^2+....+20^2=1540

Đặt A = 1^2+2^2+...+10^2 = 385

-> A x 2^2 =1^2 x 2^2 + 2^2 x 2^2 +....+ 10^2 x 2^2 = 385 x 2^2

-> A x 2^2 = (1x2)^2 + (2x2)^2 +...+ (10x2)^2 = 385 x 2^2

-> A x 2^2 = 2^2 + 4^2 +...+ 20^2 = 385 x 2^2

-> A x 2^2 = S = 385 x 2^2 = 385 x 4 =  1540

S = 2^2 + 4^2+6^2+.....+20^2 
= ( 1.2 ) ^2 + ( 2.2)^2 +.....+ (2.10 ) ^2 
= 2^2( 1^2 + 2^2 +.....+ 10^2 ) 
=2^2 . 385 
 = 4 . 385 = 1540

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

\(=\left(1.2\right)^2+\left(2.2\right)^2+\left(2.3\right)^2+...+\left(2.10\right)^2\)

\(=1^2.2^2+2^2.2^2+2^2.3^2+....+2^2.10^2\)

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

Mà \(1^2+2^2+3^2+...+10^2=385\)

Nên \(S=2^2.385=4.385=1540\)

\(S=2^2+4^2+....+20^2=?\)

\(=\left(2.1\right)^2+\left(2.2\right)^2+\left(2.3\right)^2+....+\left(2.10\right)^2\)

\(=2^2.1^2+2^2.2^2+2^2.2^3+...+2^2.10^2\)

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

\(=2^2.385\)

\(=4.385\)

\(=1540\)

S=2²+4²+...+20²

=> 1/2 .S=1²+2²+...+10²

=> 1/2 .S=385

=> S = 385 . 2

=> S = 770

P=(1.3)²+...+(10.3)

   =3²(1²+...+10²)

   =9.385 = 3465

Đặt T = 1² + 2² + ... + 10² = 385

=> T x 2² = 1². 2² + 2². 2² + ... + 10².2² = 385. 2²

=> T x 2² = (1.2)² + (2. 2)² + ... + (10.2)² = 385. 2² 

=> T x 2² = (2)² + (4)² + ... + (20)² = 385. 2² 

=> T x 2² = S = 385. 2² 

=> S = 385 x 4

olm duyệt

ung ho mk nha cac bn ^_^

\(\$\sqrt{a}\)

A = \(2^2.\left(1^2+2^2+3^2+...+10^2\right)=4.385=1540\)

B=\(3^2.\left(1^2+2^2+3^2+...+10^2\right)=385.9=3465\)

S= 1540 

 cần lời giải mình sẽ cho nhé 

gọi tổng đầu là A

2²A=(1.2)²+(2.2)²+...+(2.10)²

4A = 2²+4²+6²+..+20²=> 4A = S = 385 .4 = 1460

Ta thấy:
2² = 1² * 2²
4² = 2² * 2²
6² = 3² * 2²
.................
20² = 10² * 2²
Vậy:
S = 1² * 2² + 2² * 2² + 3² * 2² + ... + 10² * 2²
S = 2² * ( 1² + 2² + 3² + ... + 10² )
S = 4 * 385
S = 1540

=1540

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 ~

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

S=2²+4²+6²+...+20²

S=(2*1)²+(2*2)²+(2*3)²+...+(2*10)²

=2²*1²+2²*2²+...+2²*10²=2²(1²+2²+3²+...+10²)=4*385=1540

Vậy S=1540