A) \[{{1}^{2}}+{{2}^{2}}+.....+{{n}^{2}}<{{n}^{3}}/3\]
B) \[{{1}^{2}}+{{2}^{2}}+.....+{{n}^{2}}={{n}^{3}}/3\]
C) \[{{1}^{2}}+{{2}^{2}}+.....+{{n}^{2}}>{{n}^{3}}\]
D) \[{{1}^{2}}+{{2}^{2}}+.....+{{n}^{2}}>{{n}^{3}}/3\]
Correct Answer: D
Solution :
[d]:\[{{1}^{2}}+{{2}^{2}}+...+{{n}^{2}}=\frac{n(n+1)(2n+1)}{6}\] \[=\frac{n\times (n+1)(n+1/2)}{3}>\frac{n.n.n}{3}=\frac{{{n}^{3}}}{3}\] [\[\because \]\[n+1>n\]and \[n+1/2>n\]]
You need to login to perform this action.
You will be redirected in
3 sec
