Let $\xi_1, \xi_2, \cdots, \xi_n$ be indeterminates. Define the following indeterminates: $s_k := \sum\limits_{i=1}^n\xi_i^k, 1\le k <\infty ,$ $\sigma_k := \sum\limits_{1\le i_1
How to show $ \prod\limits_{i=1}^n(1-\xi_it)=1-\sigma_1t+\sigma_2t^2-\cdots+(-1)^n\sigma_nt^n=\exp\left(-\sum\limits_{j=1}^\infty s_j\frac{t^j}{j}\right)?$
Thanks.