a: A=3^2(1^2+2^2+...+10^2)

=9*385

=3465

b: B=2^3(1^3+2^3+...+10^3)

=8*3025

=24200

b. S=(2+4+6+...+19+20)^2

P=(3+6+9+...+30)^2

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

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

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

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

\(=2^2.385\)

\(=4.385\)

\(=1540\)

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

ai nhanh nhất,đúng nhất mình  cho

Lời giải:

$S=10^2+(10.2)^2+(10.3)^2+...+(10.9)^2+(10.10)^2$

$=10^2(1^2+2^2+3^2+...+9^2+10^2)$

$=100.385=38500$

S=1540

dung ko ta

Ta có : \(1^2+2^2+3^2+......+10^2=385\)

\(2^2\left(1^2+2^2+3^2+......+10^2\right)=2^2.385\)

\(2^2+4^2+6^2+.....+20^2=4.385\)

\(2^2+4^2+6^2+.....+20^2=1540\)

S = 1540

k cho mk nha

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

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