Question

Does the sequence a1=1, a(n+1) = (an -1)/(an+1) converge?

Answer 1

As defined, the sequence is not convergent.


`\begin{case}a_1=1\\a_(n+1)=(a_n-1)/(a_n+1)&\text{for }n\ge2\end{cases}`

`\implies a_2=(1-1)/(1+1)=0`

`\implies a_3=(0-1)/(0+1)=-1`

`\implies a_4=(-1-1)/(-1+1)=-\frac20`

but the last term is undefined.