1. ## Limit of sequence

This sequence is strictly increasing (monotonic, already proved).

3 is an upper bound on this sequence(already proved). Therefore I know that this sequence converges to a Limit A which is <= 3.

My question is knowing all this, how do I find the Limit A? I.E. What the series converges to, the exact number.

Thanks,

Len

2. Originally Posted by Len

This sequence is strictly increasing (monotonic, already proved).

3 is an upper bound on this sequence(already proved). Therefore I know that this sequence converges to a Limit A which is <= 3.

My question is knowing all this, how do I find the Limit A? I.E. What the series converges to, the exact number.

Thanks,

Len
Let $\displaystyle \lim b_n = L$. then, of course, $\displaystyle \lim b_{n + 1} = L$ as well.

thus, take $\displaystyle b_{n + 1} = 3 - \frac 1{b_n}$

take the limit of both sides.

$\displaystyle \lim b_{n + 1} = \lim \left(3 - \frac 1{b_n} \right)$

$\displaystyle \Rightarrow L = 3 - \frac 1L$

i leave the rest to you