For given positive real numbers \(a_1,\ldots,a_k\) and for each integer n≥k, let \(a_{n+1}\) be the geometric mean of \( a_n, a_{n-1}, a_{n-2}, \ldots, a_{n-k+1}\). Prove that \( \lim_{n\to\infty} a_n\) exists and compute this limit.
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2012-5 Iterative geometric mean,
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for each integer n>k가 아니라 n>=k 아닌가요?
@홍승한: 고쳤습니다. 지적해주셔서 감사합니다.