What is the weighted mean of the first n natu | vedclass

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(B) The weighted mean is given by the formula: $	ext{Weighted Mean} = \frac{\sum x_i w_i}{\sum w_i}$.Here,$x_i = i$ and $w_i = i$ for $i = 1, 2, \ldo

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$\frac{2n + 1}{3}$

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(B) The weighted mean is given by the formula: $	ext{Weighted Mean} = \frac{\sum x_i w_i}{\sum w_i}$.Here,$x_i = i$ and $w_i = i$ for $i = 1, 2, \ldots, n$.So,$	ext{Weighted Mean} = \frac{\sum_{i=1}^n i \cdot i}{\sum_{i=1}^n i} = \frac{\sum_{i=1}^n i^2}{\sum_{i=1}^n i}$.Using the standard summation formulas $\sum_{i=1}^n i^2 = \frac{n(n+1)(2n+1)}{6}$ and $\sum_{i=1}^n i = \frac{n(n+1)}{2}$,we get:$	ext{Weighted Mean} = \frac{\frac{n(n+1)(2n+1)}{6}}{\frac{n(n+1)}{2}} = \frac{2n+1}{3}$.

What is the weighted mean of the first $n$ natural numbers when the weights are equal to the corresponding natural numbers?

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