Just a very small query, I am currently looking at the solutions to a question, and the final step is:
$c$ $\sum_{k=1}^\infty p^k$ = $\frac{cp}{1-p}$
Is this correct? I thought this formula only held when it went from k = 0 to infinity?
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3Yes, it is correct. And $\displaystyle c\sum_{k=0}^\infty p^k=\frac c{1-p}\ne\frac{cp}{1-p}$. – José Carlos Santos Jul 24 '22 at 10:57
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The formula holds for any starting value for k, as long as the common ratio is between -1 and 1. – insipidintegrator Jul 24 '22 at 11:40