Question

đố: biết rằng : 1\(^{^{ }2}\) + 2 mũ 2 + 3 mủ 2 + ...+ 10 mũ 2 = 385, đố em tính nhanh đc tổng :

S = 2 mũ 2 + 4 mũ 2 + 6 mũ 2 + ...+20 mũ 2

Answer 1

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

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

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

\(=385.4=1540\)

Vậy S = 1540

Answer 2

Giải:

Đặt \(A=1^2+2^2+...+10^2=385\)

\(\Rightarrow A.2^2=1^2.2^2+2^2.2^2+...+10^2.2^2=385.2^2\)

\(\Rightarrow A.2^2=\left(1.2\right)^2+\left(2.2\right)^2+...+\left(10.2\right)^2=385.2^2\)

\(\Rightarrow A.2^2=\left(2\right)^2+\left(4\right)^2+...+\left(20\right)^2=385.2^2\)

\(\Rightarrow A.2^2=S=385.2^2\)

\(\Rightarrow S=385.4\)

\(\Rightarrow S=1540\)

Answer 3

Ta có: 1² + 2² + 3² + ... + 10² = 385

S = 2² + 4² + 6² + ... + 20²

= (1.2)² + (2.2)² + (3.2)² + ... + (10.2)²

= 1².2² + 2².2² + 3².2² + ... + 10².2²

= 2² (1² + 2² + 3² + ... + 10²)

= 4.385 = 1540

Answer 4

Ta có : S = \(2^2\) + \(4^2\) + \(6^2\) + ...... + \(20^2\)

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

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

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

= 4 . 385

= 1540

Vậy S = 1540