Ramanujan also made a series for calculating pi. The series itself as we can see has a denominator of each term is a power of 2. By this obeservation, we can see how the partial sum of the series can be expressed as binary. By using Sterling's approximation, Ramanujan came up with \(\binom{2n}{n}\equiv\frac{2^{2n}}{\sqrt{\pi n}}\). By taking a closer look, we can see how the nth term in the series makes a rational number. The rational number has a numerator that can be expressed as \(2^{6n}\) along with the denominator as \(2^{-6n-4}\). Overall we can see tha the series will converge quickly and we will be left with a series that looks like \(\frac{1}{\pi}=\frac{5}{16}+\frac{376}{65536}+\frac{19224}{268435456}+...\) And in the end, Ramanujan was able to come up with an approximation for pi.