Weird nested sequence! \(V_{ij} \)
Number Theory
Level
4
Consider the sequence \(3,18,243,...n×3^{2^{n-1}}\)
If this sequence is enclosed in nested square roots upto infinite terms i.e. if
\(\sqrt{3+\sqrt{18+\sqrt{243+...}}}=k\),
Find the value of \(\left\lceil{k}\right\rceil\).
Note:
This problem is similar to the below problem.
by
Vinay Sipani