Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum. (If an answer does not exist, enter DNE.) 1 + 0.5 + 0.25 + 0.125 + ...

Convergent. The sum is 2.

Step-by-step explanation:

First let's find the rate of the series. We can find it by dividing one term by the term before:

So the rate of the series is 0.5. The series is convergent if the rate is between 0 and 1, so this series is convergent.

We can find its sum with the following equation:

Where a_1 is the first term and r is the rate.

So we have that:

The sum of the series is 2.

there is no grid

step-by-step explanation:

the population of other specie of birds will decline or other specie of birds will find some alternate source of food to survive.

explanation:

according to the competitive exclusion principle, which is also known as gause's law, two specie living in the same niche and feeding on the same resource cannot co-exist stably.

as we have well studied the theory of natural selection which states that only those organisms survive which have better tendency to compete for food and adapt to the environmental conditions.

coming towards the question, what wi ll happen when one species outcompetes the other for the small fish , the other specie will not get enough food and will start to die or decline in population. eventually either other specie needs to find another alternative food source for itself or migrate at some other location where there is less competition otherwise it will just not exist anymore at that niche.

hope it !