Purchase Solution

Sum of infinite geometric series

Not what you're looking for?

Ask Custom Question

A regular hexagon is inscribed in a circle of radius 100. The area of that hexagon outside the square is shaded. Another circle is inscribed in the hexagon, and hexagon is inscribed in the second circle. The area of the second circle which lies outside the hexagon is shaded. This process continues to infinity.
What is the sum of all shaded areas?

Radius of 1 = 100
Radius of 2 = ______
Radius of 3 = _______
Radius of 4 = ________
Side of hexagon 1st =_________
Side of hexagon 2nd = ________
Side of hexagon 3rd = ________
Side of hexagon 4th = _______
Area of Circle 1 = ________
Area of Circle 2 = ________
Area of Crcle 3 =________
Area of Circle 4 = _______
Area of Hexagon 1 = _______
Area of Hexagon 2 =______
Area of Hexagon 3 = ______
Area of Hexagon 4 = _________
Difference of 1st =_________
Difference of 2nd =_________
Difference of 3rd =_________
Difference of 4th =________

Each new one is _________of the previous area.
Sum of all areas = ___________

Is there any relationship concerning the areas as the number of sides of the inscribed figure increases? If so what would you predict would be the area sum for 8 or 9 sides?_________

Purchase this Solution
Solution Summary

This is an infinite geometric series question using the hexagons and circles inscribed inside of each other.

Solution Preview

see attachment

The sum of an infinite Geometric Series
________________________________________
A regular hexagon is inscribed in a circle of radius 100. The area of that hexagon outside the square is shaded. Another circle is inscribed in the hexagon, and hexagon is inscribed in the second circle. The area of the second circle which lies outside the hexagon is shaded. This ...

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
Purchase this Solution
Free BrainMass Quizzes
Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Probability Quiz

Some questions on probability

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

View More Free Quizzes
Related BrainMass Solutions

  • Geometric Series and Sums

    Solution There are two possibilities to determine sum of two geometric series.

  • Sum of geometric series

    The above sum can be written as summation terms in expression is an expansion of The sum of above series is given by = 1 Thank you! The formula for sum of both finite and infinite geometric series is given.

  • Geometric series

    The series can be written as : 2/3 + (2/3)*1/3 + (2/3)*1/3^2 + (2/3)*1/3^3....... The sum to an infinite Geometric series is given by : a/(1-r) where a = first term r = rate.

  • Multipliers and Geometric Series: Application to U.S. Economy

    This process of spending continues and results in an infinite geometric series as follows: 1, 0.90, 0.90^2, 0.90^3, 0.90^4.... The sum of this infinite geometric series is called the multiplier.

  • Expected Value Sample Solution

    We simply replace the winnings amount in the calculation of the expectation. a) The summation becomes E(X) = sum c^k * p(x) = sum (c/2)^k = c/2 + (c/2)^2 + (c/2)^3 + ... This is an infinite geometric series with common ratio c/2.

  • Series Calculation and Its Convergent Properity

    This is the sum of an infinite geometric series with a = 0.6381 and r = 0.0000 6381/0.6381= 0.0001 Fraction = a/(1 - r) = 0.6381/(1 - 0.0001) =0.6381/0.9999=6381/9999 The solution gives detailed steps on finding the sum of integer series and determining

  • Closed Form for an Infinite Series

    Does the series converge for x=i? This series is a geometric series and so its infinite sum is 1/(1-x) and this is its closed form.

  • a convergent geometric series with a=100 and r=1/10

    The sum of a geometric series is S = a/(1-r) = 100/(1-1/10) = 100(10/9) = 1000/9 =111.11 feet This solution demonstrates a convergent geometric series with a=100 and r=1/10.

  • Infinite Series : Geometric Progression

    45851 Infinite Series: Geometric Progression Summation of series from n=2 to infinity of (pi/4)^(n/2) I don't know if I should set the whole thing up as a power of e and then calculate it, or calculate it as geometric series.

View More Related Solutions