Spivak's Calculus Ch.2 Problem 2(i)

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Homework Help Overview

The problem involves finding a formula for the sum of the first n odd numbers, represented as Σ(2i-1) = 1+3+5+...+(2n-1). The context is within a calculus framework, specifically referencing a hint related to the sum of the first 2n natural numbers.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the relationship between the sum of odd numbers and the sum of natural numbers, questioning how to connect the hint provided with the original expression. There is an exploration of the difference between these two sums.

Discussion Status

The discussion is ongoing, with participants offering hints and exploring connections between the sums. One participant reports a moment of clarity regarding the hints, suggesting that some productive direction has emerged.

Contextual Notes

Participants are navigating the significance of the hints provided and how they relate to the problem statement. There is an emphasis on understanding rather than seeking direct answers.

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Homework Statement


Find a formula for Σ(2i-1) = 1+3+5+...+(2n-1)

Hint: What does the expression have to do with 1+2+3+...+2n?

Homework Equations

The Attempt at a Solution


I have tried to solve this on my own for about a day now, and I am having trouble understanding the significance of the hint. I don't want an answer, just advice on how to connect the hint and the original expression.[/B]
 
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Hint: let ##S = 1 + 2 + ... + 2n## and ##Y = 1 + 3 + 5 + ... + (2n - 1)##

Then what is ##S - Y##?
 
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axmls said:
Hint: let ##S = 1 + 2 + ... + 2n## and ##Y = 1 + 3 + 5 + ... + (2n - 1)##

Then what is ##S - Y##?

Also: how can you find ##S-Y## in terms of ##n##?
 
Last edited:
Thanks guys, i finally had an epiphany earlier today with your hints.
 
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