Với mọi số nguyên \(n\ge1\), đẳng thức nào sau đây đúng?
\(1^2+2^2+3^2+...+\left(n-1\right)^2+n^2=\dfrac{n\left(n+1\right)\left(2n+1\right)}{12}\).\(1.2+2.3+...+n\left(n+1\right)=\dfrac{n\left(n+1\right)\left(n+2\right)}{3}\).\(1.2+2.3+...+n\left(n+1\right)=\dfrac{n^2+3n+2}{3}\).\(1^2+2^2+3^2+...+\left(n-1\right)^2+n^2=\dfrac{\left(n+1\right)\left(2n+1\right)}{7}\).