prove that: Σ_(n=1) ^∞ tan^( −1) ( (1/F_( n) ) ).tan^( −1) ( (1/F_( n+1) ) )= (π^( 2) /8) Fibonacci numbers


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Question Number 158322 by mnjuly1970 last updated on 02/Nov/21

$p r o v e t h a t :$ $\underset{n = 1}{\sum^{\infty}} {t a n}^{- 1} (\frac{1}{F_{n}}) . {t a n}^{- 1} (\frac{1}{F_{n + 1}}) = \frac{π^{2}}{8}$ $F i b o n a c c i n u m b e r s$
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