A) \[{{1}^{2}}+{{2}^{2}}+...+{{n}^{2}}<\frac{{{n}^{3}}}{3}\]
B) \[{{1}^{2}}+{{2}^{2}}+...+{{n}^{2}}=\frac{{{n}^{3}}}{3}\]
C) \[{{1}^{2}}+{{2}^{2}}+...+{{n}^{2}}>{{n}^{3}}\]
D) \[{{1}^{2}}+{{2}^{2}}+...+{{n}^{2}}>\frac{{{n}^{3}}}{3}\]
Correct Answer: D
Solution :
| by taking option [d] | |
| When\[~n=1\] | then \[1>\frac{1}{3}\] [True] |
| When\[n=2\] | then \[5>\frac{8}{3},\] [True] |
| When\[n=3\] | then \[14>9,\] [True] |
| When\[n=4\] | then \[30>\frac{64}{3}=21.33\] [True] |
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