Hi everyone,

I've a little trouble with a small exercice.

So, given the equation $\displaystyle x^n+x=1$, it can ben easily shown that $\displaystyle \displaystyle \exists ! x_n \in \mathbb{R}^+ / x_n^n + x_n = 1$.

I also prooved that the sequence $\displaystyle (x_n)_{n > 0}$ is convergent and its limit is $\displaystyle l=1$.

Now, the question is : Find an asymptotic equivalent of $\displaystyle x_n - l$. And this is what I have trouble with.

I've tried some thing, for example, we know that $\displaystyle x_n - 1 = - x_n^n$ but this expression do not seem to bring something good.

So, I don't want the whole answer, but just the little trick that I've not seen and which can end this question.

Thanks for reading me, and sorry if my english is little bit bad,

Hugo.