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The expression as given doesn't make much sense. I think you're trying to describe an infinitely nested radical. We can express this recursively by
Then you want to know the value of
if it exists.
To show the limit exists and that converges to some limit, we can try showing that the sequence is bounded and monotonic.
Boundedness: It's true that . Suppose
. Then
. So by induction,
is bounded above by 7 for all
.
Monontonicity: We have and
. It should be quite clear that
. Suppose
. Then
. So by induction,
is monotonically increasing.
Then because is bounded above and strictly increasing, the limit exists. Call it
. Now,
Solve for :
We omit because our analysis above showed that
must be positive.
So the value of the infinitely nested radical is 7.
Student is wrong An exterior angle of a triangle can be adjacent to the right angle of a right triangle, so an exterior angle can be a right angle.
<h3>What is exterior angle?</h3>The Exterior Angle is the angle between any side of a shape, and a line extended from the next side.
The student make an error he states that the exterior angle of a triangle can never be a right angle.
The correct answer will be option D that is An exterior angle of a triangle can be adjacent to the right angle of a right triangle, so an exterior angle can be a right angle.I have also attached the diagram of the triangle for better understanding.
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