This is a homework question, so I would prefer hints/suggestions as opposed to full-out solutions.
Given the Lagrange polynomials $\ell_i(x)=\displaystyle\prod_{j=0;j\neq i}^n\frac{x-x_j}{x_i-x_j}$ for equally-spaced interpolation points $a=x_0,x_1,\ldots,x_{n-1},x_n=b$ (over the interval $[a,b]$), I am to find the upper and lower bound for the Lebesgue constant $\Lambda=\displaystyle\max_{x\in[a,b]}\sum_{i=0}^n\big|\ell_i(x)\big|$ for $n=2,3,4$.
I have used the substitution $x=a+\frac{s(b-a)}{n}$ where $s\in[0,n]$ and deduced that $\ell_i(x)=\displaystyle\prod_{j=0;j\neq i}^n\frac{s-j}{i-j}$. I also have noticed that (by using the triangle inequality) that $\Lambda\geq1$ (at least for $n=2$) and for the same value of $n$, I found that $\Lambda\leq 3$. I'm not sure these are the types of values being sought after, though, since a quick check on the Wikipedia page gives that $\Lambda_n\sim\frac{2^{n+1}}{e\log n}$ as $n\to\infty$.
I guess my question is really: am I on the correct track? (I can give more information if needed, I just didn't want to make a TL;DR post.) Thanks in advance!