How to proof the following identity: $ \sum_{k=0}^{n} \prod_{j=0\\j\neq k}^{n} \frac{t_k}{t_k-t_j} =1$
Is this algebraic identity obvious? $\sum_{i=1}^n \prod_{j\neq i} {\lambda_j\over \lambda_j-\lambda_i}=1$