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

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 ^_^

\(\$\sqrt{a}\)

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

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

 2^2 = (1.2)^2 
4^2 = (2.2)^2 
..... 
Vế dưới = (1.2)^2 + (2.2)^2 + .........+ (9.2)^2 + (10.2)^2 = 2^2.(1^2 + 2^2 + 3^2 + .....+ 9^2 + 10^2) 
= 4(385) = 1540

2^2 4^2 6^2 8^2 ..... 18^2 20^2 
= (1x2)^2 (2x2)^2 (3x2)^2 (4x2)^2 ..... (9x2)^2 (10x2)^2 
= 1^2 x 2^2 2^2 x 2^2 3^2 x 2^2 4^2 x 2^2 ..... 9^2 x 2^2 10^2 x 2^2 
= (1^2 2^2 3^2 4^2 ..... 9^2 10^2) x 2^2 
= 385 x 2^2 = 385 x 4 = 1540

tran thi nhan : copy trên mạng

Vì 1²+2²+3²+...+10² = 385
Mà  S = 2²+4²+6²+...+20²
= 2².(1²+2²+3²+...+10²) = 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 + 6^2 + .. +20^2

S = 2^2 + 2^2.2^2 + 2^2.3^2 + ... + 2^2 . 10^2

S = 2^2 ( 1 + 2^2 + 3^2 + .. + 10^2)

S = 4 . 385

S = 1540 

Ta có : 1² + 2² + 3² + .....+ 10² = 385

=> 2²(1² + 2² + 3² + .....+ 10²) = 2².385

=>2² + 4² + 6² + .....+ 20² = 4.385

=> S = 1540 

=> 2²(1² + 2² + 3² + .....+ 10²) = 2².385

=>2² + 4² + 6² + .....+ 20² = 4.385

=> S = 1540