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 :)

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- May 7th 2011, 12:20 AMbrumby_3Summation
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 :) - May 7th 2011, 03:26 AMPlato
You need to study

*SPECIAL SUMS* - May 7th 2011, 04:32 AMtopsquark
- May 7th 2011, 05:41 AMSoroban
Hello, brumby_3!

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.

Quote:

. .

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 . . .

. . . .

- May 7th 2011, 05:57 AMProve It
http://i22.photobucket.com/albums/b3...ofintegers.jpg

http://i22.photobucket.com/albums/b3...mofsquares.jpg

http://i22.photobucket.com/albums/b3...sumofcubes.jpg

From these diagrams it should be clear that

http://quicklatex.com/cache3/ql_4d49...2f0548e_l3.png

See if you can evaluate your sums now... - May 7th 2011, 06:05 AMtopsquark
The general idea was for the OP to look them up him/herself....

-Dan - May 7th 2011, 06:23 AMProve It