Question

The total number of fungal spores can be found using an infinite geometric series where a1 = 8 and the common ratio is 4. Find the sum of this infinite series that will be the upper limit of the fungal spores.

Answer 1

Answer:

This infinite geometric series is divergent and thus we cannot find the sum. The sum is infinity.

Step-by-step explanation:

There are two types of geometric series: convergent and divergent.

The sum of an infinite geometric sequence is given by the formula:

Sum = $\frac{a}{1-r}$

Where,

r is the common ratio and

$|r|$

If absolute value of r is NOT less than 1, then the series is divergent and sum cannot be found.

For our given problem, $r=4$ ,  clearly  $|4|=4$ , which is NOT less than 1, so the series is divergent and sum cannot be found.

Answer 2

The formula for infinite geometric series is equal to a1 / (1-r) where in this problem a1 is equal to 8 and r is equal to 4. In this case, r is not equal to less than 1. This means the sum should be infinity and cannot be determined definitely.