Ta có: \(\dfrac{\left[\left(2x-2\right):2+1\right].2x+2}{2}=210\)
\(\Rightarrow\left[2\left(x-1\right):2+1\right].2\left(x+1\right)=420\)
\(\Rightarrow x-1+1.\left[2\left(x+1\right)\right]=420\)
\(\Rightarrow x.2\left(x+1\right)=420\)
\(\Rightarrow x\left(x+1\right)=210\)
\(\Rightarrow x\left(x+1\right)=14.15\)
\(\Rightarrow x=14\)
Vậy \(x=14\)
Ta có:
2 + 4 + 6 + 8 + ... + 2x
= 2.1 + 2.2 + 2.3 + 2.4 +.....+ 2x
= 2(1 + 2 + 3 + 4 + ..... + x)
Vì 2 + 4 + 6 + 8 + ... + 2x = 210
\(\Rightarrow\) 2(1 + 2 + 3 + 4 + ..... + x) = 210
\(\Rightarrow\) 1 + 2 + 3 + 4 + ..... + x = 210 : 2 = 105
\(\Rightarrow\) \(\dfrac{\left(x+1\right)x}{2}\) = 105
\(\Rightarrow\) (x + 1)x = 210
\(\Rightarrow\) (x + 1)x = 15 . 14
\(\Rightarrow\) x = 14
ta co:2+4+6+8+...+2x=210
2*(1+2+3+4+...+x)=210
(1+2+3+4+...+x)=210/2=105
(1+x)*x/2=105
(1+x)*x=105*2=210
vì 1+x và x là hai số tự nhiên liên tiếp nên x=14
vậy x=14
