- #1
Justabeginner
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Homework Statement
Notice that [itex] ln [∏(k=1)^n a^k] = Ʃ_(k=1)^n * ln (a_k) [/itex]
I couldn't get the LaTeX right on this ^ But k=1 is below the product sign, and n is above. And (a^k) is the formula.
From this, as well as some calculus, calculate that:
[itex] lim as n->∞ ∏_(k=1)^n e^\frac{k^2}{n^3} [/itex]
For this ^ the limit is as n tends to infinity, and k=1 is below the product sign, and n is above the product sign.
Homework Equations
The Attempt at a Solution
The first equation I think is an example of the distributive property? However, I am not sure how to show that the limit would tend to infinity for the second part, without applying actual values? (When the limit becomes 1/0 is infinity?)
Thank you.