Question Number 101822 by john santu last updated on 04/Jul/20

lim_(n→∞) ((φ^(n+1) −(−φ)^(−n−1) )/(φ^n −(−φ)^(−n) )) =   (JS ⊛)

Answered by bobhans last updated on 05/Jul/20

φ = (((√5) +1)/2) > 1 ; lim_(n→∞)  (−φ)^(−n) = lim_(n→∞) (1/((−φ)^n )) = 0  Then lim_(n→∞) ((φ^(n+1) −(−φ)^(−n−1) )/(φ^n −(−φ)^(−n) )) = lim_(n→∞) (φ^(n+1) /φ^n ) = φ  = (((√5) +1)/2) (Bob− )