
a.
Find an infinite geometric series to represents the sum of the perimeters of all the
a.

Answer to Problem 78STP
The geometric series is
Explanation of Solution
Given: It is given in the question that there is an equilateral triangle ABC that have a perimeter
Concept Used:
In this, use the concept of infinite geometric series formula
Calculation:
Since, in this the perimeter is increasing after then after so first term will be
And it is seen that the perimeter is three halves that and it is forever this,
Conclusion:
The series is
b.
Calculate the sum of the perimeters of all the triangles.
b.

Answer to Problem 78STP
The perimeter of the triangles is
Explanation of Solution
Given:
It is given in the question that there is an equilateral triangle ABC that have a perimeter
Concept Used:
In this, use the concept of understanding the question and the series and if the same thing is goes on then it becomes infinite.
Calculation:
Here, the series is
Since, the sum is growing , it is not converging to a particular point because the number being rasied to a power is greater than one, the sum will grow.
So, the perimeter of all the triangles is infinite
Conclusion:
The perimeter is
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