Answer:
Step-by-step explanation:
we know that
The area of the shaded region is equal to the area of triangle plus the area of semicircle
so
we have
Find the height of the right triangle applying the Pythagorean Theorem
The radius of the semicircle is half the height of triangle
substitute in the formula
Option A: The sum for the infinite geometric series does not exist
Explanation:
The given series is
We need to determine the sum for the infinite geometric series.
<u>Common ratio:</u>
The common difference for the given infinite series is given by
Thus, the common difference is
<u>Sum of the infinite series:</u>
The sum of the infinite series can be determined using the formula,
where
Since, the value of r is 3 and the value of r does not lie in the limit
Hence, the sum for the given infinite geometric series does not exist.
Therefore, Option A is the correct answer.