(a) Show that if lim_n→∞a_2n = L and lim_n→∞a_2n+1 =− L, then {an} is convergent and lim_n→∞a_n = L.

(b) If a₁ 1 and

find the first eight terms of the sequence {an}. Then use part (a) to show that lim_n→∞ an = √2 . This gives the continued fraction expansion

Transcribed Image Text:

1 Ar±1 =1 + 1+ an