Thread Subject: nth term

1 1 1 1 1 1 1 1
- - - - - - - -
3 12 30 60 105 168 252 360

The third series of fractions above are worked out using the
formula n(n+1)/2-n.I need to finish off the series of
fractions up to the ninth series. I am stuggling to find the
formula for the fourth series of fractions and beyond.

"Mark Mortlock" <arty_guitarist@yahoo.co.uk> wrote in message <fpv7u2
$1us$1@fred.mathworks.com>...
> 1 1 1 1 1 1 1 1
> - - - - - - - -
> 3 12 30 60 105 168 252 360
>
> The third series of fractions above are worked out using the
> formula n(n+1)/2-n.I need to finish off the series of
> fractions up to the ninth series. I am stuggling to find the
> formula for the fourth series of fractions and beyond.
--------
  I am not at all sure what you are asking us, Mark. You seen to be
interchanging the terminologies for 'terms' and 'series'.

  However, I do recommend that you start with the series of integers you
show here: 3, 12, 30, 60, etc. and take their first differences, then their
second differences, and finally their third differences. Then try to work
backwards and deduce what that next unknown ninth value in that original
series would reasonably be. Do the same for the tenth, eleventh, etc. I give
you one further hint: when you finally do arrive at a general expression for
the n-th value in this, it will turn out to be a third degree polynomial in n. All
you have to do is figure out what its four coefficients must be.

Roger Stafford

"Mark Mortlock" <arty_guitarist@yahoo.co.uk> wrote in message
<fpv7u2$1us$1@fred.mathworks.com>...
> 1 1 1 1 1 1 1 1
> - - - - - - - -
> 3 12 30 60 105 168 252 360
>
> The third series of fractions above are worked out using the
> formula n(n+1)/2-n.I need to finish off the series of
> fractions up to the ninth series. I am stuggling to find the
> formula for the fourth series of fractions and beyond.

What have you tried?

What does diff tell you about that series?
How about higher order differences? What
order polynomial is necessary to represent
these terms exactly?

John