Writing an expression as a product of products

Question

I am currently dealing with the following expression: $$\left(\prod_{i=1}^{N-1}(\lambda_N-\lambda_i)\right)\left(\prod_{i=1}^{N-2}(\lambda_{N-1}-\lambda_i)\right)\cdots (\lambda_2-\lambda_1)$$ Is there a way to simplify this even further? I am relatively unfamiliar with notation of the sort: $$\sum\sum \text{or} \prod\prod$$ How may I write it in this form?

Answer 1

Observe that for every integer $2 \leq k \leq N$ the $k$th term takes the form $$\prod_{i=1}^{k-1}(\lambda_{k} - \lambda_{i}),$$ so the desired form is obtained by multiplying all the $N-1$ terms together, which is $$\prod_{k=2}^{N}\prod_{i=1}^{k-1}(\lambda_{k} - \lambda_{i}).$$