In a lab experiment, 2000 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to do
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Looks like your function is
Rewrite it as
Recall that for , we have
If we replace with
, we get
By the ratio test, the series converges if
Solving for gives the interval of convergence,
We can confirm that the interval is open by checking for convergence at the endpoints; we'd find that the resulting series diverge.