This question was uploaded on 23/11/21 on social media accounts.
Solution:
Given Equation:
\[S = 1 + \frac12 + \frac1{2.4} + \frac1{2.4.6} + \frac1{2.4.6.8} + ....\]
\[S = 1 + \frac{\left(\frac12\right)}{1!} + \frac{\left(\frac12\right)^2}{2!} + \frac{\left(\frac12\right)^3}{3!} + \frac{\left(\frac12\right)^4}{4!} + ....\]
We know that:
\[e^x = 1 + \frac{x}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!} + \frac{x^4}{4!} + ....\]
\[\Rightarrow S = e^{1/2} = \sqrt e\]
