This should be correct?

[vcesuccess]

Write the summation notation of


I wrote

[TrueTears]

That wouldn't work since

I'd do this:

[vcesuccess]

Yours is correct?

[TrueTears]

Well when you expand my one you get .

[QuantumJG]

That wouldn't work since

I'd do this:

Yep TT is right! It would be great if you could find the whole polynomial from the summation operator. If vcesuccess had of subtracted 1/3 from his summation it would yield the quadratic.

I can't wait until I do real analysis and look at:

convergence:



divergence:

[TrueTears]

That wouldn't work since

I'd do this:

Yep TT is right! It would be great if you could find the whole polynomial from the summation operator. If vcesuccess had of subtracted 1/3 from his summation it would yield the quadratic.

I can't wait until I do real analysis and look at:

convergence:



divergence:

Haha I've been doing quite a bit of convergence and divergence, they're really fun!

[enwiabe]

Write the summation notation of


I wrote

Oh so close!

Should be:



The way I approached it was with the insight that the geometric series of co-efficients was 1, 2, 4 (I.E. multiplying/dividing by 2 each time), and that these would increase by 1 power each time, which was the same increase as the powers of the polynomials.

EDIT: *whacks head* or more simply:

[Collin Li]

Are there an infinite number of ways to write a summation notation for that, or something? Or, is there always a way to write something in summation notation (without being cheap and just going i=1 to 1, and writing the expression)?

[kyzoo]

Is this even part of Methods?

[humph]

Are there an infinite number of ways to write a summation notation for that, or something? Or, is there always a way to write something in summation notation (without being cheap and just going i=1 to 1, and writing the expression)?

Well this

isn't really summation notation, because there's an extra term (a constant at the end). And this

is just this

after reversing the direction of summation.
For a general series, you often can't say more than just for some sequence , as there might not be a suitably "nice" pattern that allows us to give some closed form expression for . For example, if is just some random sequence of real numbers, then with probability 1 there's going to be no closed-form way of writing it (as a combination of geometric series, arithmetic series, in terms of some elementary function, etc.).