1. ## Help! What are the patterns...

I have a tricky question here....

Please just feed in any comment, anything you can spot that I can't

I have been asked to compare the formula of Sygma (k=1 until n value) of k, Sygma (k=1 until n value) of k(k+1) and Sygma (k=1 until n value) of k(k+1)(k+2)?

Hence comparing these...

Sygma (k=1 until n value) of k[/B] = 1/2 n(n+1)

Sygma (k=1 until n value) of k(k+1)[/B] = 1/3 n(n+1)(n+2)

Sygma (k=1 until n value) of k(k+1)(k+2) [/B] = 1/4 n(n+1)(n+2)(n+3)

I have been asked to comment on these as much as I possibly can Can anyone help?

2. Originally Posted by Natasha
I have a tricky question here....

Please just feed in any comment, anything you can spot that I can't

I have been asked to compare the formula of Sygma (k=1 until n value) of k, Sygma (k=1 until n value) of k(k+1) and Sygma (k=1 until n value) of k(k+1)(k+2)?

Hence comparing these...

Sygma (k=1 until n value) of k[/B] = 1/2 n(n+1)

Sygma (k=1 until n value) of k(k+1)[/B] = 1/3 n(n+1)(n+2)

Sygma (k=1 until n value) of k(k+1)(k+2) [/B] = 1/4 n(n+1)(n+2)(n+3)

I have been asked to comment on these as much as I possibly can Can anyone help?
1.Look at the right-hand-sides of your three equations

2. Do you notice anything about the fractions which occur
just before the first n in each of these?

3. Look at the part on the right-hand-side after the fraction,
is there something you can do to one of these to get the next?

4. Do the things you have noticed generalise?

5. Can these sums be rearranged to give any other sums which
might be of interest?

RonL