Evaluate these summations.
a) N(E)k=1 (k-k^3)
b) N-1(E)k=1 (k^2/N^2)
Note that (E) is the summation symbol.
Not sure how to do these. Help would be appreciated
These can be solved with basic algebra, but the process is long and tedious.
Don't know anyone who'd want to do it . . . Okay, it's me.
Take the differences of consecutive terms in the Partial Sums sequence.
Then take the differences of the differences . . . and so on.
We see that the 4th differences are constant.
This tells us that the generating function is of the 4th degree.
The general quartic function is: .
Use the first 5 terms of the sequence and set up this system:
Solve the system: .
. . Hence: .
This can be drastically simplified . . .
. . . .