Respuesta :
Given geomatric series 0.79 + 0.079 + 0.0079 + 0.00079 + 0.000079 +.....
First term of the given geomatric series = 0.79.
Common ratio = [tex]\frac{0.079 }{0.79}[/tex] = [tex]\frac{1}{10}[/tex]
Sum of infinite geometric series is given by formula
S∞ = [tex]\frac{a}{1-r}[/tex]
Where, a is the first term and r is the common ratio.
Plgging valus of a and r in above formula, we get
S∞ = [tex]\frac{0.79}{1-\frac{1}{10} }[/tex]
=[tex]\frac{0.79}{\frac{10-1}{10} }[/tex]
=[tex]\frac{0.79}{\frac{9}{10}}[/tex]
= [tex]0.79\times\frac{10}{9}=\frac{79}{10} \times\frac{10}{9} = \frac{79}{9}[/tex]
Therefore,
Sum of the infinite geometric series = [tex]\frac{79}{9}[/tex]
