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 :
| [d] 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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