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Determine the value(s) of k for which p is a probability mass function. Note that n is a positive integer. $$p(x) = kx, x = 1,2,3,... ,n$$

According to the solution manual, $k=\frac{2}{n(n+1)}$, but I don't know how to arrive at this answer. I know that because p is a probability mass function, $$\sum_{x=1}^n kx=1$$ but I'm not sure where to go from there.

LadymadeStar
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1 Answers1

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$\begin{align*} \sum_{x = 1}^n kx &= 1\\ k \left ( \sum_{x = 1}^n x \right ) &= 1\\ \end{align*}$

$\sum \limits_{x = 1}^n x = \frac{n(n+1)}{2}$ is one of the standard formulas for series.

rims
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