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July 23rd, 2011, 11:20 AM   #1
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Problem in limits of summations

I have this expression:

.

I am going to set and , so I have to change summations' limits

I know that the first summation will be:



because and .

and that n should not appear. But that i can't understand is what happens to limits of the other summations and and why.

I know that i have to use these inequalities:
.

Any idea?
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July 23rd, 2011, 04:23 PM   #2
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Re: Problem in limits of summations

There is a problem with . If you swap with you end up with

, which isn't going to work.
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July 23rd, 2011, 04:43 PM   #3
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Re: Problem in limits of summations

I am not going to swap with .
My final goal is the expression with summations to end up like that:
and
so what about the limits?
Thank you for your reply and I am grateful to help me!
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July 23rd, 2011, 04:47 PM   #4
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Re: Problem in limits of summations

You've got the assignment Then you state that you are going to use



What happens to ?
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July 23rd, 2011, 04:57 PM   #5
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Re: Problem in limits of summations

As I explained because of:

takes numbers from 1 until and then

will take numbers from 1 until .
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