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I have a problem whereby I want to calculate the limit of a sequence of determinants of matrices of increasing dimensions using the DiscreteLimit command. To illustrate this, I use an example with a known exact limit. Consider the following

f[n_] = Det[SparseArray[Table[{i, i} -> 1 + 1/n, {i, 1, n}]]];
DiscreteLimit[f[n], n -> Infinity]

We are really calculating $\lim_{n\to\infty}(1+\frac{1}n{})^n$ which we know to be $e$, but running the code won't give me this. Is there any way of calculating this limit starting from the function $f$ defined as the determinant of the matrices. Thanks.

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  • $\begingroup$ Normally I would suggest FindSequenceFunction[] for this, but even in your simple case, it seems to choke. $\endgroup$
    – J. M.'s lack of A.I. ♦
    Jan 27, 2020 at 12:07
  • $\begingroup$ In some simple cases, you might be able to find a recurrence relationship between the determinants for different values of n $\endgroup$
    – mikado
    Jan 27, 2020 at 19:16

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