Answer:
See below
Step-by-step explanation:
If you notice a pattern, 15*3/5=9, 9*3/5=27/5, and 27/5*3/5=81/25. So this is an infinite geometric series.
So the common ratio is 3/5 where the first term is 15 and n=1, so the summation notation would be [tex]\sum _{n=1}^{\infty }\:15\left(\frac{3}{5}\right)^n[/tex]
To find the sum of an infinite geometric series, we use the formula S(n)=a1/1-r where r is the common ratio:
S(n)=15/1-3/5
S(n)=15/2/5
S(n)=75/2
So the sum of the infinite geometric series is therefore 75/2 or 37.5
Hope this helped!
