a)
[tex]S = \sum_{i=1}^{n} \frac{1}{\sqrt{i+1} + \sqrt{i}} = \sum_{i=1}^{n} \frac{\sqrt{i+1} - \sqrt{i}}{i+1 - i} = \sum_{i=1}^{n} \sqrt{i+1} - \sqrt{i} = \sqrt{n+1} - 1[/tex]
b)
[tex]\sqrt{n+1} - 1 = 2018\\\sqrt{n+1} = 2019\\n + 1 = 2019^2\\n = 2019^2 - 1 = 4,076,360[/tex]
