Answer:
Final answer is [tex]\frac{200}{11}[/tex].
Step-by-step explanation:
Given infinite geometric series is [tex]20-2+\frac{1}{5}-\cdot\cdot\cdot[/tex].
First term [tex]a_1=20[/tex],
Second term [tex]a_2=-2[/tex],
Third term [tex]a_3=\frac{1}{5}[/tex]
then common ratio using first and 2nd terms
[tex]r=\frac{a_2}{a_1}=-\frac{2}{20}=-0.1[/tex]
common ratio using 2nd and 3rd term
[tex]r=\frac{a_3}{a_2}=\frac{\left(\frac{1}{5}\right)}{-2}=-0.1[/tex]
Hence it is confirmed that it is an infinite geometric series
Now plug these values into infinite sum formula of geometric series:
[tex]S_{\infty}=\frac{a_1}{1-r}=\frac{20}{1-\left(-0.1\right)}=\frac{20}{1.1}=\frac{200}{11}[/tex]
Hence final answer is [tex]\frac{200}{11}[/tex].
