Can We Apply AM-GM?

Calculus Level 4

limnAnGn\large \displaystyle \lim_{n \to \infty} \dfrac {A_n}{G_n}

Let a1,a2,,ana_1, a_2, \ldots, a_n be an arithmetic progression composed solely of distinct positive reals.

Also, let AnA_n denote its arithmetic mean and GnG_n denote its geometric mean.

What is the value of the above limit to 3 decimal places?

If you think the limit doesn't exist, write -13.37 as your answer.


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