Answer:
The sum in sigma form is [tex]\sum_{i=1}^{\infty}42(\frac{3}{4})^{i}[/tex]
The upper limit of the population is 168.
Step-by-step explanation:
We are given that,
Population of dragonfly is represented by the series with,
First term, [tex]a_{1}=42[/tex]
Common ratio, [tex]r=\frac{3}{4}[/tex]
So, we see that,
The sum in sigma form is given by [tex]\sum_{i=1}^{\infty}a_{1}r^{i}[/tex]
That is, [tex]\sum_{i=1}^{\infty}42(\frac{3}{4})^{i}[/tex]
Now, the infinite sum of the series is [tex]S=\frac{a_1}{1-r}[/tex]
So, the sum is [tex]S=\frac{42}{1-\frac{3}{4}}[/tex]
i.e. [tex]S=\frac{42\times 4}{4-3}[/tex]
i.e. [tex]S=\frac{168}{1}[/tex]
Thus, the upper limit of the population is 168.
