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Mar 8, 2017 at 18:24 comment added Iosif Pinelis Using Stirling's formula, it is indeed easy to see that $\frac{1}{n}(\log(a_{n}^n)-\log(b_{n}^n))$ converges to $(a+1)\ln\frac{a+1}e-(b+1)\ln\frac{b+1}e$. However, this is not what the problem is about. Please review the definition of $p_n$ and $q_n$.
Mar 8, 2017 at 18:17 history answered Anna Petrova CC BY-SA 3.0