A sequence was defined by a equation The sequence was defined by the equations:
$${a}_{1}=a\left(\in R \right),{a}_{n+1}=\frac{2{{a}_{n}}^{3}}{1+{{a}_{n}}^{4}},n\geq 1.$$
show that
$\left(a \right)$The given sequence is convergent. (whatever $a\in \mathbf{R}$)
$\left(b \right)$
Finding its all possible limit.
$\left(c \right)$
Dividing $\mathbf{R}$ into several intervals,such that if the initial value ${a}_{1}$ lies in the same interval,then sequence $\begin{Bmatrix}
{a}_{n}
\end{Bmatrix}$ has the same limit.

Some thoughts on (a)
If $a>0$ use the AM-GM inequality to show that
$a_{n+1}\leq a_{n}$ for all n.
In this case we also have
$a_{n}\geq 0$  for all n.
What is that telling you about convergence?
