Binomial theorem differentiation (1 Viewer)

[iLean]

My teacher said we aren't allowed to differentiate the sigma in binomial theorem. She said something about it not being mathematically correct to just differentiate a sigma so instead she told us to expand it first and then differentiate.
My tutor on the other hand said that its perfectly valid to bring the sigma out before the d/dx and continue.

Who is correct?

 

[Sy123]

It is mathematically incorrect to do so if the sigma refers to an infinite sum, i.e.:



Whereas:



This is because firstly:



And, the sigma notation is simply that, a notation for what ... is.

Tell this to your teacher, if she still does not accept, ask her why it is justified to assume that differentiation is applicable in a sum where it exists a

 

[Carrotsticks]

My teacher said we aren't allowed to differentiate the sigma in binomial theorem. She said something about it not being mathematically correct to just differentiate a sigma so instead she told us to expand it first and then differentiate.
My tutor on the other hand said that its perfectly valid to bring the sigma out before the d/dx and continue.

Who is correct?

Binomial theorem has partial sums (finite sums up to say N).

Differentiation of a finite sum is perfectly legal, sigma notation and writing it out are equivalent things. One is just a concise way of writing the other, it is not some operation or anything.

Your tutor is correct, your teacher is incorrect.

 

[Carrotsticks]

It is mathematically incorrect to do so if the sigma refers to an infinite sum, i.e.:

Note that they CAN be equal in the case that the series converges absolutely.

 

[Sy123]

Note that they CAN be equal in the case that the series converges absolutely.

Yep, I was merely pointing out that at her level the operation can not be justified

 

[iLean]

Thanks guys, I'll let you know what happens

 

[iLean]

Alright it's allowed now

When solving for the coefficient of a term, can I use this method:

As opposed to this: