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

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

Bài 1:

A = 1 + 3 + 3² + ... + 3¹⁰⁰

=> 3A = 3 + 3² + ... + 3¹⁰¹

=> 2A = 3¹⁰¹ - 1

=> A = \(\frac{3^{101}-1}{2}\)

B = 1 + 4² + 4⁴ + ... + 4¹⁰⁰

=> 8B = 4² + 4⁴ + ... + 4¹⁰²

=> 7B = 4¹⁰² - 1

=> B = \(\frac{4^{102}-1}{7}\)

Bài 2:

a) S₁ = 2² + 4² + ... + 20²

=> S₁ = 2²(1+2²+...+10²)

=> S₁ = 2².385

=> S₁ = 1540

b) S₂ = 100² + 200² + ... + 1000²

=> S₂ = 100²(1+2²+...+10²)

=> S₂ = 100².385

=> S₂ = 3850000

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

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

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

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

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

Lời giải:

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

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

$=100.385=38500$

4.385=1540

cmr m=125&,fklmgmni

= 1540 nhé

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