Question

The population of a local species of dragonfly can be found using an infinite geometric series where a1 = 48 and the common ratio is one fourth. Write the sum in sigma notation and calculate the sum that will be the upper limit of this population.

Answer 1

Answer:

The sigma notation would look like this:

∞

Σ       48(1/4)^i-1

i = 1

Step-by-step explanation:

I can't seem to find a good way to make it more connected so I'll just have to tell you. The ∞ is above the ∑, while the i = 1 is under it. That is all one thing. The rest is followed as normal, and it is all next to the ∑

Answer 2

Answer:  

The sum of the given geometric series and its sigma notation is given below :

Step-by-step explanation:

First term, a = 48

$\text{Common ratio, r = }\frac{1}{4}$

The series is given to be geometric series and the sum of geometric series is given by :

$S_n=\frac{a}{1-r}\\\\\implies S_n=\frac{48}{1-\frac{1}{4}}\\\\\implies S_n = 64$

And for sigma notation,

$Sum = \sum_{i=1}^{\infty}a\cdot(r)^i-1\\\\\implies Sum = \sum_{i=1}^{\infty} 48\cdot(\frac{1}{4})^{i-1}$