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Consider the sequence 3,18,243,...n×32n−13,18,243,...n×3^{2^{n-1}}3,18,243,...n×32n−1
If this sequence is enclosed in nested square roots upto infinite terms i.e. if
3+18+243+...=k\sqrt{3+\sqrt{18+\sqrt{243+...}}}=k3+18+243+...=k,
Find the value of ⌈k⌉\left\lceil{k}\right\rceil⌈k⌉.
This problem is similar to the below problem.
Nested Radicals
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