- #1

- 2,012

- 1

## Homework Statement

can someone help me with only if part of Problem 2?

http://www.math.cornell.edu/~putnam/ineqs.pdf

I can prove that quantity is less than or equal to n, but I cannot get it leq to 1?

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter ehrenfest
- Start date

- #1

- 2,012

- 1

can someone help me with only if part of Problem 2?

http://www.math.cornell.edu/~putnam/ineqs.pdf

I can prove that quantity is less than or equal to n, but I cannot get it leq to 1?

- #2

- 15,393

- 686

- #3

- 2,012

- 1

- #4

- 15,393

- 686

You want to leave expressions involving {*r*_{i}} on both sides of the inequality.

- #5

- 2,012

- 1

- #6

- 15,393

- 686

You don't need Cauchy-Schwartz. You are on the right track. Set each x_{i} to r_{i}.

- #7

- 2,012

- 1

- #8

- 15,393

- 686

To be completely rigorous you also have to handle the special case where the division in the final step is not valid. This case is trivial, so to speak.

- #9

- 2,012

- 1

When r is a null vector its length is certainly less than or equal to 1.

- #10

- 15,393

- 686

- #11

- 2,012

- 1

I agree. Thanks.

Share: