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Are these the same formula? (Maclaurin's)

The textbook says that there are 5 formulae for Maclaurin's series that will be given in the formula book. 4 in the formula book are the same as ones in the textbook but one I just cannot decipher haha.

In the textbook, the 5th formula is given as

but in the formula book, it's given as

I have no idea what I'm looking at haha. Can someone translate?

Reply 1

stephen1011

Why is this labelled as AS?

Reply 2

username3855958

Original post by stephen1011

Why is this labelled as AS?

Because I'm doing AS Further Maths

Reply 3

RDKGames

Study Forum Helper

Original post by katietelliii

....

Maclaurin series for a GENERAL function

f(x)

is said to be

f(x) = f(0)+xf'(0)+\dfrac{x^2}{2!}f''(0) + \ldots + \dfrac{x^n}{n!}f^{(n)}(0) + \ldots

(which is what you got boxed in the second image)

But the textbook provides some important functions which have ALREADY had this formula applied (to make it simpler for the student since they are the most common ones to pop up and be used for more complex expressions), and these are precisely all the ones in the first image.

So the expansion of

(1+x)^n

is indeed the same as the expansion of

f(x)

with

f(x) = (1+x)^n

(edited 5 years ago)

Reply 4

username3855958

Original post by RDKGames

Maclaurin series for a GENERAL function

f(x)

is said to be

f(x) = f(0)+xf'(0)+\dfrac{x^2}{2!}f''(0) + \ldots + \dfrac{x^n}{n!}f^{(n)}(0) + \ldots

(which is what you got boxed in the second image)

But the textbook provides some important functions which have ALREADY had this formula applied (to make it simpler for the student since they are the most common ones to pop up), and these are precisely all the ones in the first image.

So the expansion of

(1+x)^n

is indeed the same as the expansion of

f(x)

with

f(x) = (1+x)^n

I guess that formatting is just a bit too advanced for me haha. I only first saw the formula book a week ago and we've never covered that formatting. I guess I'll just try to memorise the one given in the textbook 😅 Thank you for explaining!