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- September 7th 2009, 12:23 PMflower3real analysis
- September 7th 2009, 01:05 PMPlato
If then

- September 7th 2009, 03:18 PMJG89
Just as you said, .

That's a finite sum, and so for large enough k, the entire sum should go to 0. But if we're trying to prove that for**all**J, K > k, then isn't it possible to hold K fixed and take J so large that the sum doesn't actually approach 0?

Let me know if my question isn't clear enough. - September 7th 2009, 03:36 PMPlato
- September 7th 2009, 03:45 PMJG89
But the sum converges to 3/2. So .

Aren't we trying to show that |x_J - x_K| goes to 0? - September 7th 2009, 04:00 PMPlato
- September 7th 2009, 06:16 PMJG89
Wow, I had worked that out but didn't realize I was working out the partial sums...no excuses though, that was a silly mistake. Thanks for the help Plato