We observe that the above progression possess a common ratio. So it is a geometric progression.
Common ratio = \(\cfrac{\frac{2}{5^2}}{\frac{2}{5}}\) = \(\frac{3}{10}\)
Sum of infinite GP = \(\frac{a}{1-r}\) ,where a is the first term and r is the common ratio.
Note: We can only use the above formula if |r|<1
Clearly, a = \(\frac{2}{5}\) and r = \(\frac{3}{10}\)
⇒ sum = \(\cfrac{\frac{2}{5}}{1- \frac{3}{10}} = \cfrac{4}{7}\)
