Concept explainers
(a)
To find: The infinite series.
(a)
Answer to Problem 68RE
Explanation of Solution
Given information:
Punching out Triangles this exercise refers to the “right side up” equilateral triangle with sides of length 2b in the accompanying figure.
Formula used:
Area of equilateral triangle of side of length
Calculation:
Area of equilateral triangle of side of length
Now, the sequence or area removed from the original triangle is,
Conclusion:
(b)
To find: The sum of the infinite series.
(b)
Answer to Problem 68RE
The sum of the series is
Explanation of Solution
Formula used:
Geometric progression is used.
Calculation:
It is a geometric progression with initial term is
Therefore, sum of the series is
Conclusion:
The sum of the series is
(c)
To analyse: if original part of every triangle is removed.
(c)
Answer to Problem 68RE
No. Not every point is removed
Explanation of Solution
Formula used:
The triangle is considered.
Calculation:
No. Not every point is removed. For example, the vertices of the triangle are not removed.
Conclusion:
No. Not every point is removed
Chapter 10 Solutions
Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
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