22+42+62+82+.....+202
=22.(1+22+32+42+...+102)
=4.385
=1540
= 10 ,12,14,16,18
them so 2 o tren nua nhe nguyen ngoc son
\(2^2+4^2+6^2+...+20^2\)
\(=2^2\left(1^2+2^2+3^2+...+10^2\right)\)
\(=4.\frac{10\left(10+1\right)\left(2.10+1\right)}{6}\)
\(=4.385=1540\)
nha!
2^2+4^2+6^2+8^2+.....+20^2=2^2.(1+2^2+4^2+6^2+.....+10^2)=4.(1^2+2^2+4^2+6^2+.....+10^2)=4.385=1450
Đặt \(S=2^2+4^2+6^2+...+20^2=2^2.1^2+2^2.2^2+2^2.3^2+...+2^2.10^2\)
<=> \(S=4.\left(1^2+2^2+3^2+...+10^2\right)\)
<=> \(\frac{S}{4}=1^2+2^2+...+10^2\)
<=>\(\frac{S}{4}=1.\left(2-1\right)+2\left(3-1\right)+...+10\left(11-1\right)\)
<=> \(\frac{S}{4}=1.2+2.3+...+10.11-\left(1+2+...+10\right)\)
Mặt khác:
Đặt A = 1.2 + 2.3 +...+10.11 => 3A = 1.2.(3-0) + 2.3.(4-1) + ... + 10.11.(12-9)=> 3A = 1.2.3 + 2.3.4 - 1.2.3 + ... + 10.11.12 - 9.10.11
=> 3A = 10.11.12 => A=10.11.4 = 440
1+2+3+...+10 = 55=> S/4 = 440 + 55 = 495
=> S = 495 * 4 = 1980