Answer:
The sum of geometric series 6 - 4 + 8/3 - 16/9 + 32/17 is 4.0416
Step-by-step explanation:
We need to find the sum of geometric series 6 - 4 + 8/3 - 16/9 + 32/17
The formula used to find sum of geometric series is [tex]S_n=\frac{a(1-r^n)}{1-r}[/tex]
where a is 1st term, n is number of terms and r is common ratio
so, in the given geometric series 6 - 4 + 8/3 - 16/9 + 32/17 we have
First Term a=6
Common ratio r= -0.6
Number of terms n= 5
Putting values in formula to find sum of given geometric series
[tex]S_n=\frac{a(1-r^n)}{1-r}\\S_n=\frac{6(1-(-0.6)^5 )}{1-(-0.6)}\\S_n=\frac{6(1-(-0.07776))}{1+0.6}\\S_n=\frac{6(1+0.07776)}{1.6}\\S_n=\frac{6.46656}{1.6}\\S_n=4.0416[/tex]
So, the sum of geometric series 6 - 4 + 8/3 - 16/9 + 32/17 is 4.0416
