Generating Functions · Catalan Numbers
Lesson 3
Using the formula \[\sqrt{1+x}= \sum_{n=0}^{\infty}\frac{(-1)^n}{(1-2n)4^n}\binom{2n}{n}x^{n},\] expand \(\mathcal{S}(x)=\frac{1 - \sqrt{1-4x}}{2x}\):
Generating Functions · Catalan Numbers
Using the formula \[\sqrt{1+x}= \sum_{n=0}^{\infty}\frac{(-1)^n}{(1-2n)4^n}\binom{2n}{n}x^{n},\] expand \(\mathcal{S}(x)=\frac{1 - \sqrt{1-4x}}{2x}\):