Induction Mathematical Proof and Odd and Even Powers
Not what you're looking for?
Show that any positive integral power of (√2 - 1) can be written in the form √N -
√(N-1) , where N is a positive integer.
Hint: Use mathematical induction and consider separately the odd and even powers of (√2 - 1).
We need to prove the following statement.
Statement : For any positive n, (√2 - 1)ⁿ = √N - √(N-1) for some positive integer N.
Note: N depends on n.
Before we prove the above statement, we will prove a theorem below.
Please see attachment for full question.
Purchase this Solution
Solution Summary
This is a proof regarding integral powers. The induction mathematical proof and odd and even powers.
Solution Preview
Because,
(sqrt(2) - 1)^n = sqrt(2a^2) - ...
Education
- BEng, Allahabad University, India
- MSc , Pune University, India
- PhD (IP), Pune University, India
Recent Feedback
- " In question 2, you incorrectly add in the $3.00 dividend that was just paid to determine the value of the stock price using the dividend discount model. In question 4 response, it should have also been recognized that dividend discount models are not useful if any of the parameters used in the model are inaccurate. "
- "feedback: fail to recognize the operating cash flow will not begin until the end of year 3."
- "Answer was correct"
- "Great thanks"
- "Perfect solution..thank you"
Purchase this Solution
Free BrainMass Quizzes
Solving quadratic inequalities
This quiz test you on how well you are familiar with solving quadratic inequalities.
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.
Probability Quiz
Some questions on probability