$$\sum_{k=1}^n{2^{k^k}}$$
I couldn't find anything on this with a simple Google search so is it not trivial? If yes then can someone link some resources/Wikipedia page where I could read more? (can't find myself since I don't know the name of this)
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3For an approximate answer, just take the last term. The terms grow so fast that the next to last is negligible by comparison with the last. For example, at $n=10$ we have $2^{10^{10}}\approx 10^{3010299966}$ is too large for Alpha to do, but $2^{9^9} \approx 10^{116625118}$ – Ross Millikan Aug 04 '21 at 03:42
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2Related: Sum of the form $r+r^2+r^4+\dots+r^{2^k} = \sum_{i=1}^k r^{2^i}$ – Dave L. Renfro Aug 04 '21 at 06:20