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humanaction
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Homework Statement
Prove xn-yn=(x-y)(xn-1+xn-2y+…+xyn-2+yn-1
Homework Equations
12 basic properties of numbers
The Attempt at a Solution
I'm all good except I don't see why x2yn-2-xn-2y2=0
humanaction said:Homework Statement
Prove xn-yn=(x-y)(xn-1+xn-2y+…+xyn-2+yn-1
Homework Equations
12 basic properties of numbers
The Attempt at a Solution
I'm all good except I don't see why x2yn-2-xn-2y2=0
Ray Vickson said:This is not true unless x = y (or sometimes x = -y as well, depending on n). Anyway, why do you write this? It has nothing at all to do with the original question.
Are you perhaps confusing (xn-1+xn-2y+…+xyn-2+yn-1) with (xn-1+xn-2y+xyn-2+yn-1)?humanaction said:Homework Statement
Prove xn-yn=(x-y)(xn-1+xn-2y+…+xyn-2+yn-1
Homework Equations
12 basic properties of numbers
The Attempt at a Solution
I'm all good except I don't see why x2yn-2-xn-2y2=0
humanaction said:thank you for your information. my uni allows me to test out of and earn credit for up to calculus iii. i will look into those books. in the meantime, could you try to explain this ellipsis to me? i haven't run into any problems with the other questions from this chapter, I've just never done an algebraic operation of an ellipsis before.
Spivak Calculus Ch 1 Q1 (v) refers to the first question in Chapter 1 of the book "Calculus" by Michael Spivak. This question asks the reader to prove a specific theorem related to limits.
This question is important because it introduces one of the fundamental concepts in calculus - limits. Understanding limits is crucial in solving more complex problems in calculus and other branches of mathematics.
The difficulty level of this question may vary for different individuals. However, it is generally considered to be a challenging question that requires a solid understanding of basic calculus concepts.
Some strategies for solving this question include reviewing the definition of a limit, understanding the given theorem, and using algebraic manipulation and properties of limits to prove the theorem.
Yes, there are many resources available such as online forums, study guides, and tutoring services that can provide assistance in solving this question. Additionally, the book "Calculus" by Michael Spivak contains detailed explanations and examples that can aid in understanding and solving this question.