# How do you find the 4-th partial sum of the infinite series sum_(n=1)^oo(1/sqrt(n)-1/sqrt(n+1)) ?

${S}_{4} = \left(\frac{1}{\sqrt{1}} - \frac{1}{\sqrt{2}}\right) + \left(\frac{1}{\sqrt{2}} - \frac{1}{\sqrt{3}}\right) + \left(\frac{1}{\sqrt{3}} - \frac{1}{\sqrt{4}}\right) + \left(\frac{1}{\sqrt{4}} - \frac{1}{\sqrt{5}}\right)$
$= 1 + \left(- \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}}\right) + \left(- \frac{1}{\sqrt{3}} + \frac{1}{\sqrt{3}}\right) + \left(- \frac{1}{\sqrt{4}} + \frac{1}{\sqrt{4}}\right) - \frac{1}{\sqrt{5}}$
$= 1 - \frac{1}{\sqrt{5}}$