Question

x_1=3/2, x_(n+1)=3/(4-x_n)

prove that the series x_n converges and find its limit.

Answer 1

the sequence is

3/2, 6/5, 15/14, ...

I don't see how it can converge, since each term is greater than 1.

Answer 2

I can answer the second part. Obviously it converges to 1.

But i do not know how to prove it...

I do not know if it is legit but maybe since you know the limit is 1 use definition: For every n>N |a_n-1|<epsilon

and prove this way.

Answer 3

its no proof but you could see the results are: 3/2, 6/5, 15/14,42/41,123/122,366/365,1095/1094,3282/3281,9843/9842.

as you could see it comes closer and closer to 1 therfore its limit is 1.

Answer 4

sorry. My bad. I was thinking we wanted the series to converge, not the sequence.