general sums

[tommy1729]

There exists a formula for iterated sums.

If

\( Sum_n({ a_n }) = S_n \)
\( S_0 = 0 \)
\( S_n = S_{n - 1} + a_n \)

Then

\( Sum_n^k({ a_n }) = \sum_{j=1}^{n} { {k + (n - j) - 1}\choose{k - 1} } \cdot a_j \)

thats great !

now all we need to do is take the continuum sum of that.

where did you get that formula btw ? newton ? gauss ?

thanks

regards

tommy1729