Mathematical induction/pascal triangle
Not what you're looking for?
Please help me with the attached pre-calculus questions.
1. Use mathematical induction to prove that 6 is a factor of n (n + 1)(n + 2).
2. Use mathematical induction to prove 1^2 + 3^2 + 5^2 + . . . + (2n - 1)^2 = n (4n^2 - 1) / 3.
3. Expand (2x - y)^6 using binomial coefficients and then evaluate each coefficient.
Example: the first term is 6 chose 0 (2x)^6 (-y)^0 = 64x^6
4. Interpret what the result in problem 3 tells us about construction the next row of the Pascal triangle:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
5. Find the equation of the circle that has its center at the focus of the parabola X^2 - 4x + 6y - 20 = 0 and that is tangent to the parabola at its vertex. Also sketch both curves.
6. Find the equation of the Ellipse whose foci coincide with the foci of the hyperbola x^2 - 3y^2 - 2x - 12y + 1 = 0 and whose eccentricity is the reciprocal of that of the hyperbola.
Purchase this Solution
Solution Summary
This solution includes step by step solutions of problems on Mathematical Induction, pascal triangle and finding equation of ellipse and circle.
Education
- BSc, Meerut University
- MSc, Meerut University
- MPhil, Institute of Advanced Studies
- MSc, AIT
Recent Feedback
- "Perfect, thank you so much!!! I will definitely request you in the future! You are amazing!"
- "Thank you. "
- "Thank you so much I have two more that I need your help with if your available."
- "Thank you, I was wondering why you rejected me the first time."
- "Thanks again."
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.
Probability Quiz
Some questions on probability
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts
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.