Respuesta :
The sum of the infinite geometric series
[tex] a+ar+ar^2+... [/tex] where [tex] a [/tex] is the first term and [tex] r [/tex] common ratio [tex] -1<r<1 [/tex] is [tex] \frac{a}{1-r} [/tex].
Here the given series is [tex] \frac{1}{7} +\frac{1}{49} +\frac{1}{343} +... [/tex].
Here [tex] a=1,r=\frac{1}{7} [/tex]. The sum of the infinite geometric series is
[tex] \frac{1}{1-1/7} =\frac{7}{6} [/tex]
