A) \[\frac{n+1}{2}\]
B) \[\frac{3n(n+1)}{2(2n+1)}\]
C) \[\frac{(n+1)(2n+1)}{6}\]
D) \[\frac{n(n+1)}{2}\]
Correct Answer: B
Solution :
Weighted mean = \[\frac{{{1.1}^{2}}+{{2.2}^{2}}+......+n.{{n}^{2}}}{{{1}^{2}}+{{2}^{2}}+......+{{n}^{2}}}\] \[=\frac{\Sigma {{n}^{3}}}{\Sigma {{n}^{2}}}=\frac{\frac{n(n+1)}{2}\,\,\frac{n(n+1)}{2}}{\frac{n(n+1)(2n+1)}{6}}\]\[=\frac{3n(n+1)}{2(2n+1)}\].
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