Given $\;t_{r}=1^2+2^2+.......\;r^2$ and $t_{1}+t_{2}+t_{3}+...\;t_{n}=\large\frac{k}{12}\;n\;(n+1)\;(n+2)\;$ the value of k will be

Question

$(a)\;n\qquad(b)\;2n+1\qquad(c)\;3n-1\qquad(d)\;n+1$