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# C4 Binomial Expansion Help Watch

1. Hi. I'm stuck on a particular question and wondered if anyone could help. It is:

a) Find the first 5 terms in the expansion of (1+2x)^-1

I can do this, getting the answer 1 - 2x + 4x^2 - 8x^3 + 16x^4

b) Use the expansion to find an approximation to f 0.1 to -0.2 (1/1+2x) dx.

c) By evaluating the integral exactly, find an approximation for ln2.

I can do part a) fine. Also, I can do other approximations using the binomial expansion, just I have no idea where to start when it involves integrals.

Help would be much appreciated.

Thanks
2. if the power is 1 the expansion is quite easy....

the bear
3. (Original post by Marisa_Grace)
b) Use the expansion to find an approximation to f 0.1 to -0.2 (1/1+2x) dx.

seeing as you've just found the first five terms of the expansion of , which is the same as , it makes sense to substitute the expansion into the integral. so:

is approximately equal to
4. (Original post by the bear)
if the power is 1 the expansion is quite easy....

the bear
Typo lol!
5. (Original post by Pheylan)

seeing as you've just found the first five terms of the expansion of , which is the same as , it makes sense to substitute the expansion into the integral. so:

is approximately equal to
Thanks. I get that. But how would I do part c)? When I integrate exactly I get, 0.5ln2.
6. (Original post by Marisa_Grace)
Thanks. I get that. But how would I do part c)? When I integrate exactly I get, 0.5ln2.
so if , then

therefore, is approximately equal to...
7. (Original post by Marisa_Grace)
When I integrate exactly I get, 0.5ln2.
so you can equate 0.5ln2 to the value you obtained in part b) ...then double it to find ln2

the bear

8. (Original post by Pheylan)
so if , then

therefore, is approximately equal to...
Thanks again.

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Updated: December 12, 2010
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