Weierstrass product inequality

In mathematics, the Weierstrass product inequality states that,

For given real numbers 0 ≤ a₁, a₂, a₃, a₄, ..., a_n ≤ 1

$(1-a_{1})(1-a_{2})(1-a_{3})(1-a_{4})....(1-a_{n})\geq 1-S_{n}.$

$(1+a_{1})(1+a_{2})(1+a_{3})(1+a_{4})....(1+a_{n})\geq 1+S_{n}.$

Where,$S_{n}=a_{1}+a_{2}+a_{3}+a_{4}+....+a_{n}.$

The inequality is named after the German mathematician Karl Weierstrass. It can be proved by mathematical induction.