Hello, I was not sure if this belonged in the precalculus or calculus section so i hope no one minds that i posted it here. This is a problem that has completely lost me. http://img76.imageshack.us/img76/9191/continuousfractionrg3.gif [Broken] T1 = 1 + 1 T1 = 1+ (1/1+1) T3 = 1+ (1/(1+1/1+1) and so on I have been able to draw a generalized formula for Tn+1 in terms of Tn and that is: [PLAIN]http://img76.imageshack.us/img76/3978/continuousfraction2fg8.gif [Broken] i realized that as n increases to infinity, (Tn+1) - Tn converges towards 0 There i wrote Tn = Tn+1 and inserting this into [PLAIN]http://img76.imageshack.us/img76/3978/continuousfraction2fg8.gif [Broken] you get http://img76.imageshack.us/img76/1003/continuousfraction3nu9.gif [Broken] Therefore An exact value for the continued fraction will be considering Tn = x : x^2 - x - 1 = 0 so the exact value is: http://img76.imageshack.us/img76/3245/continuousfraction4tw6.gif [Broken] Now, Considering http://img161.imageshack.us/img161/691/continuousfraction5az5.gif [Broken] For any value of k, I am supposed to determine a generalized statement for the exact value of any such continued fraction. For which values of k does this hold true and how do i know? Can anyone please help me with this, i got so far and do not want to give up. Any tips? anything.