1-1-pi-2-1-pi-1-2-1-pi-2-2-1-1-1-pi-1-2-1-pi-2-2-1-1-pi-Prove-or-disprove-

Question Number 137347 by Dwaipayan Shikari last updated on 01/Apr/21

\frac{1}{1 + \frac{π^{2}}{1 + \frac{{(π + 1)}^{2}}{1 + \frac{{(π + 2)}^{2}}{1 + \dots}}}} + \frac{1}{1 + \frac{{(π + 1)}^{2}}{1 + \frac{{(π + 2)}^{2}}{1 + \dots}}} = \frac{1}{π}

Prove or disprove

Answered by MJS_new last updated on 01/Apr/21

t = 1 + \frac{{(π + 1)}^{2}}{1 + \frac{{(π + 2)}^{2}}{1 + \dots}} \in R [obviously]

\frac{1}{1 + \frac{π^{2}}{t}} + \frac{1}{t} = \frac{1}{π}

but this has no real solution for t \Rightarrow wrong

Commented by Dwaipayan Shikari last updated on 01/Apr/21

T h a n k s s i r!