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wasoxygen · 715 days ago · link · · parent · post: Perhaps It Is A Bad Thing That The World's Leading AI Companies Cannot Control Their AIs
Now: The sum of 0.8 to the power of n does not have a limit, because 0.8 to the power of n approaches 0 but never reaches it. As n gets larger and larger, the terms in the sum get closer and closer to 0, but they never actually reach 0, so the sum does not have a limit. However, if you are looking for the sum of the infinite geometric series with first term 0.8 and common ratio 0.8, then the sum is equal to $\frac{0.8}{1-0.8}=\frac{4}{5}$. This is because the sum of an infinite geometric series is equal to the first term divided by one minus the common ratio. LaTeX expression evaluates to (0.8)/(1 - 0.8) = 4/5.What is the limit of the sum of 0.8 to the power of n?