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

Mình cảm ơn bạn nhiều

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

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

\(B=2^2+4^2+........+20^2\)

\(B=1^2.2^2+2^2.2^2+3^2.2^2+.......+10^2.2^2\)

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

\(B=4.385\) (đề bài cho)

\(B=1540\)

B = 2^2 . (1^2 + 2^2 + ... + 10^2)

    = 4 . 385

     = 1540

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

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

S=1540

dung ko ta

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

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

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

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

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

\(2^2+4^2+6^2+..+20^2=\left(1.2\right)^2+\left(2.2\right)^2+\left(2.3\right)^2+..+\left(2.10\right)^2\)

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

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

bài này gặp nhiều rồi

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

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