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1. Hi, I have a homework question:

Show that

I split it into:

I know what the second bit is but was wondering what is.

2. (Original post by bendent1234)
Hi, I have a homework question:

Show that

I split it into:

I know what the second bit is but was wondering what is.

You know the formula for the sum from 1 to n, and it's expressed as a function of n.

If you want the sum from 1 to m, the formula would be the same, just with n replaced by m.

Similarly, for the sum from 1 to 2n, again the basic formula is the same, but just replace the n with 2n.
3. (Original post by ghostwalker)
You know the formula for the sum from 1 to n, and it's expressed as a function of n.

If you want the sum from 1 to m, the formula would be the same, just with n replaced by m.

Similarly, for the sum from 1 to 2n, again the basic formula is the same, but just replace the n with 2n.
Thanks, I thought it might be something like that but thanks for clarifying
4. (Original post by bendent1234)
Thanks, I thought it might be something like that but thanks for clarifying
You're welcome, and +rep for a well laid out question.
5. When subbing 2n into the formula to get that the answer is:

I got this to be:

This is clearly not what it should have been but I am not sure where I went wrong as my workings all seem mathematically correct
6. (Original post by bendent1234)
When subbing 2n into the formula to get that the answer is:

I got this to be:

This is clearly not what it should have been but I am not sure where I went wrong as my workings all seem mathematically correct
Your answer is correct. The question is wrong - the question should be the sum of the cube of r.
7. (Original post by Mr M)
Your answer is correct. The question is wrong - the question should be the sum of the cube of r.
Thanks for clarifying that, my teacher probably copied it onto the board wrong. I shall do the correct question
8. (Original post by bendent1234)
Thanks for clarifying that, my teacher probably copied it onto the board wrong. I shall do the correct question
I don't know if this helps for catching things like this, but the "leading term" in a summation should be the same as the leading term in what you got if you integrated instead.

e.g.

{terms smaller than n^4}. While .

This works even if you have unusual upper/lower limits as in the original question.

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