Let $y_1,\ldots,y_{n+1}$ be positive real numbers satisfying $\displaystyle{\sum_{i=1}^{n+1} \frac{1}{ny_i+1}=1}$.
Is it true that $y_1y_2\cdots y_{n+1}\geq 1$?
Added: can we determine this inequality in terms of high-school math? (e.g. Cauchy-Schwarz inequality, arithmetic mean-geometric mean inequality)