(c) 2
\(\frac{1^2+2^2+3^2+......n^2}{n}≥(1^2.2^2.3^2......n^2)^{\frac1n}\)
⇒ \(\frac{n(n+1)(2n+1)}{6n}\) > (1.2.3......n)\(\frac2n\)
⇒ \(\big(\frac{n+1}{2}\big)\big(\frac{2n+1}{3}\big) ≥(n!)^{\frac2n}\)
\(\big(\frac{n+1}{2}\big)^n\big(\frac{2n+1}{3}\big)^n ≥(n!)^2\)
⇒ k = 2.