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Question Number 103236 by Dwaipayan Shikari last updated on 13/Jul/20

$$e^{e^{e.....\mathrm{\infty }}}=?$$

Commented by Dwaipayan Shikari last updated on 13/Jul/20

$$e^{e^{e^{e^{e^{..........}}}}}=y$$$$e^y=y$$$$e^{-y}=\frac{1}{y}$$$$-{ye}^{-y}=-1$$$$-y=W_0(-1)$$$$y=-W_0(-1)=0.3181-1.333i$$

Commented by mr W last updated on 13/Jul/20

$$=\mathrm{\infty }$$

Commented by mr W last updated on 13/Jul/20

$$youappliedthesamemethodas$$$$with$$$$1+1+1+...=-\frac{1}{2}$$

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