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

[Derek Hart]

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]

 

[axmls]

Hint: let $S = 1 + 2 + ... + 2n$ and $Y = 1 + 3 + 5 + ... + (2n - 1)$

Then what is $S - Y$?

 

[Ray Vickson]

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 $n$?

 

[Derek Hart]

Thanks guys, i finally had an epiphany earlier today with your hints.