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# C4 Binomial Expansion - Question watch

1. When you have expanded the binomial expansions expressions. You have to write this part - "Expansion is valid as long as "

How do you know what to write for the |4x| < 1 and then the bit on the right of the arrow? Help me understand it.
2. The expansion of (1 + y)^n (for any* real n) is valid for |y| < 1. So if your question asks you to expand (2 + 5x)^-7, first take out the 2:

and then note it's in the form (1 + y)^n, which is valid for |y| < 1, so:

which you should normally give in the form |x| < (or maybe even >) something, so just multiply by 2/5 to get .

* An exception is when n is a positive integer, when it's actually valid for all y.
3. So basically if its (1 + y)^n, we always write |y| < 1 and then simplify it. Any good way to remember this?

And if it seems like a binomial expansion question from C2, then y is a subset of R.
4. (Original post by edward_wells90)
So basically if its (1 + y)^n, we always write |y| < 1 and then simplify it. Any good way to remember this?

And if it seems like a binomial expansion question from C2, then y is a subset of R.
Thats basically it. The poster above may have a cunning way as he is far smarter than me. However I would just remeber it like that.

Do a few "real" examples. With numbers, like you would get asked in a C4 exam. And then move on. Good luck with your exam buddy.
5. Thanks, both of you.

I've got another question:

When we get asked to find an approximation of a value and it says to substitute a suitable value of x. Do we always let x=0.01 ?

For example:
6. Find the first four terms in the expansion of . By substituting in a suitable value of x, find an approximation to .

I've got the first four terms to be:
.

What do i do next? I've let to get and subbed this value of x into the expansion but this makes no sense.
6. (Original post by edward_wells90)
Thanks, both of you.

I've got another question:

When we get asked to find an approximation of a value and it says to substitute a suitable value of x. Do we always let x=0.01 ?

For example:
6. Find the first four terms in the expansion of . By substituting in a suitable value of x, find an approximation to .

I've got the first four terms to be:
.

What do i do next? I've let to get and subbed this value of x into the expansion but this makes no sense.
7. k i tried it again and i got this:

How do i do the second part of the question?
8. (Original post by edward_wells90)
k i tried it again and i got this:

How do i do the second part of the question?
How did you get that? It dosnt look right to me. Infact I have done it myself and think its wrong. Although I'm a bit out of practise so might be wrong. Show me your working.
9. haha this time i did it here on latex and got a different answer:

10. (Original post by edward_wells90)
haha this time i did it here on latex and got a different answer:

thats right

11. Okay. But how do i do the second part of the question:

"By substituting in a suitable value of x, find an approximation to ."

I got up to this:

I see that i'm nearly there but im stuck cuz i have to get 0.99 to become 97 somehow.
13. If x=1

Can you do it now?
14. or if you let the expansion is
15. I let

and i got this:

I can't seem to get my head around this. I have to make 0.97 become 97 (but it is inside the bracket), so i have to times something by 100, but i dont understand how, or what to do!

If i multiply both sides by 100 then the left hand side would become:
but that isn't , right?
16. Via your method, you will need to multiply through by because

Unparseable or potentially dangerous latex formula. Error 4: no dvi output from LaTeX. It is likely that your formula contains syntax errors or worse.
100^{\frac{3}{2}} \times 0.97^{\frac{3}{2}} = (100\times0.97)^{\frac{3}{2}

= 97^{\frac{3}{2}}

The way I pointed out in the above post might be more 'logical.'
17. (Original post by edward_wells90)
I let

and i got this:

I can't seem to get my head around this. I have to make 0.97 become 97 (but it is inside the bracket), so i have to times something by 100, but i dont understand how, or what to do!

If i multiply both sides by 100 then the left hand side would become:
but that isn't , right?
I did say not
18. u have to put over 1000
working out is in the attachment
Attached Images

19. (Original post by tami*)
u have to put over 1000
working out is in the attachment
thanks alot, this helped. Expressing as made all the difference.
20. I need some more help on 'stating the range of values of x for which the expansions are valid':

How do i do it for:
1.

2.

-----------------------------------------------------

For question 1, if i do each of the 2 bracket separately i get:

for the first bracket:

for the second bracket:

If i combine them together, i get but this is wrong.

-----------------------------------------------------

For question 2, there are three brackets:

for the first bracket:

for the second bracket:

for the third bracket:

if i combine them, then there are no set of valid values of x lol.

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Updated: June 11, 2008
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