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

\(\Leftrightarrow2^2\left(1^2+2^2+3^2+.....+10^2\right)=2^2.385\)

\(\Leftrightarrow2^2+4^2+6^2+.....+20^2=4.385\)

\(\Leftrightarrow2^2+4^2+6^2+.....+20^2=1540\)

Sửa đề: CHo 1²+2²+...+10²=385. Tính S = 2²+4² +...+ 20²

S = 2² + 4² +...+ 20²

= (1.2)² + (2.2)² +...+ (2.10)²

= 1².2² + 2².2² +...+ 2².10²

= 2²(1² + 2² +...+ 10²)

= 4.385

= 1540

S= 1^2  .  2^2 + 2^2 . 2^2  + ... + 10^2 . 2^2
  = 4. ( 1^2 + 2^2 +...+ 10^2)  = 4 . 385 = 1540

chúc bạn học giỏi

S = 22 + 42 + 62 + ... + 202

   = (2.1)2 + (2.2)2 + (2.3)2 ... (2.10)2

   = 22.12 + 22.22 + 22.32 + ... + 22.102

   = 22 (12 + 22 + ... + 102 )

   = 4 . 385 = 1540

Ta có \(2^2+4^2+...+20^2=2^2\left(1^2+2^2+...+10^2\right)=2^2.385=1540\).

A. 1155 nha bạn 

Ta có 1² + 2² + 3² + …10² = 385

Suy ra ( 1² +2² + 3² +…+10² ) .3² = 385.3²

Do đó ta tính được A = 3² + 6² + 9² + …+30²  = 3465

1,

a,1100+(-100)=1000

b,(2017)+2010=-7

c,/-102/+36=138

d,/-1002/+(-102)=900

e,(-1002)+(-102)+515=589

A=3,85.10^6

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

=> 100²(1² + 2² + 3² + ..... + 10²) = 385

<=> 100² + 200² + 300² + .... + 1000² = 385 . 100² 

<=> 100² + 200² + 300² + .... + 1000² = 3850000

\(\left(\frac{x-y}{\sqrt{x}-\sqrt{y}}-\frac{x\sqrt{x}-y\sqrt{y}}{x-y}\right)\) ):\(\left(\frac{\left(\sqrt{x}-\sqrt{y}\right)^2+\sqrt{xy}}{\sqrt{x}+\sqrt{y}}\right)\)

=\(\frac{\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)}{\sqrt{x}-\sqrt{y}}-\frac{\left(\sqrt{x}-\sqrt{y}\right)\left(x-\sqrt{xy}+y\right)}{\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)}:\frac{x+\sqrt{xy}+y}{\sqrt{x}+\sqrt{y}}\)

=\(\left(\sqrt{x}+\sqrt{y}-\frac{x-\sqrt{xy}+y}{\sqrt{x}+\sqrt{y}}\right).\frac{\sqrt{x}+\sqrt{y}}{x+\sqrt{xy}+y}\)

=\(\frac{3\sqrt{xy}}{x+\sqrt{xy}+y}\)