.....nice calculus... prove that:: Σ_(n=0) ^∞ tan^(−1) ((1/F_n )).tan^(−1) ((1/F_(n+1) ))=(π^2 /4) F


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Question Number 137605 by mnjuly1970 last updated on 04/Apr/21

$. . . . . n i c e c a l c u l u s . . .$ $p r o v e t h a t ::$ $\underset{n = 0}{\sum^{\infty}} {t a n}^{- 1} (\frac{1}{F_{n}}) . {t a n}^{- 1} (\frac{1}{F_{n + 1}}) = \frac{π^{2}}{4}$ $F_{n} i s f i b o n a c c i s e q u e n c e . . . .$
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