summing the series n^3

Discussion in 'Mathematics' started by beedge, May 19, 2011.

1. beedgeNew commenter

I've just been glancing through my "American Scholastic Mathematics Association" (High School Division) sample questions, that they sent me yesterday.
Question 1 says "Find thes sum of the cubes of the first 16 natural numbers".
Is there a clever way of doing this? Maybe if you do these kinds of papers you're taught how to sum various series, but it's certainly nothing I know how to do.

2. Andrew JeffreyNew commenter

That's very neat Alison, and very hunble of you. If you do want to take some credit, find a couple of cubes that total another one. That should get some attention.
(I did exactly that the other day in my margin, but sadly I have recycled that particular notebook.)

3. Andrew JeffreyNew commenter

HUNBLE??? Sorry - should have been 'huMble.' of course.

I should fermat my text more carefully.

4. Joslan

Hi,
Does this mean that there are examples of how to derive the n-th term in the text books! Just being curious because from my point of view the methods I know are quite long (i.e sum to n of the cubes of natural numbers using differences leading to simultaneus eqn or using summation etc...)especially for sum of cubic numbers and I suspect the time given for the examination may not allow for such a volume of work. I can understand the inclusion of questions covering the r, r^2 and the r^3 but the cube extends this to r^4.

5. Joslan

Just correcting the question mark!!!

6. Joslan

Just reiterating what has been mentioned earlier, since you have the value of n to be 16, I expect you are only required to substitute the value of n=16 into the formula (provided by DM on the thread) that you may have been given in the formula book.

7. NRICH_Alison

We have been known to set that as a challenge to summer school students and allowing them to work on it for a few minutes before showing them the Horizon documentary on Andrew Wiles