Math Is Fun Forum

NFS1

Member

Registered: 2010-12-11

Posts: 1

Help needed on two questions!

Hi, i have recently been trying to complete an assignment of 10 mathematical questions. I have managed to answer 8 of the 10 questions but unfortunately have been unable to answer two. Can some please show me how to calculate the following as I have no idea how to attempt them. Below are the questions:

1) Given that the Maclaurin expansion of 1/1+x = 1 - x + x^2 - x^3... deduce the expansion of 1/1+cos(x) as far as the term in x^3.

2) If a>1 and n^√a = 1+x , prove that 0 < x < a/n. Deduce that n^√a --> 1 and n --> infiniti (∞). What is the corresponding result if 0 < a < 1?

Can anyone show me a step by step solution so i get a better understanding on how to answer these questions.

Thanks

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Help needed on two questions!

Hi NFS1;

1) Given that the Maclaurin expansion of 1/1+x = 1 - x + x^2 - x^3... deduce the expansion of 1/1+cos(x) as far as the term in x^3.

The idea they want is to substitute x = cos(x). Your series then becomes.

This is a slowly convergent series so do not expect much accuracy with only 3 terms.

Welcome to the forum!

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

mathgirl1997

Member

Registered: 2010-12-11

Posts: 12

Re: Help needed on two questions!

Hi NFS1:
            As bobbym said, you "deduce the expansion of 1/1+cos as far as the term".
          This is the way i find it best to figure out. If you ned more help go to aaamath,mathsisfun advanced or an advanced tutoring site.
____________________________________________________________________________________________
Hope you figure it out <3

---

"Dowell...not because its easy but because its hard "-JFK adapted by Dowell Middle School
Sincerely FSRZ <3

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Help needed on two questions!

Hi mathgirl1997;

I love being quoted but...

Welcome to the forum!

As bobbym said, you "deduce the expansion of 1/1+cos as far as the term".

Actually that is not what I said. What I said is in post #2. I am not a big fan of tutoring sites, advanced or not. I do not like the concept of charging for math on the internet. You can get the same info for nothing from anyone of a dozen free math forums. Take this one for instance, we have mathematicians, physicists, engineers, teachers and me. Now I ask you, do you need more help than that?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.