A linearly convergent sequence has the property that

This is known as Aitken’s estimate for the limit of a sequence. Compute the first four terms of the sequence

and estimate the limit of the sequence.

Transcribed Image Text:

ana(an-1-a) for all n where A is a constant and a = lim an. Show that n a=X(a, - a) an+1 Deduce that an+l - a an- a and show that a = an-l an-a an-1-a (an-an-1) antl - 2an + an-l