Binomial expansion question

Watch
Svesh
Badges: 18
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#1
Report Thread starter 2 years ago
#1
Just a quick question why is x valid for modulus of 1/2 and not 1/3?

Part b(ii)
0
reply
Svesh
Badges: 18
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#2
Report Thread starter 2 years ago
#2
Name:  binomial.png
Views: 40
Size:  19.2 KB
0
reply
RDKGames
Badges: 20
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#3
Report 2 years ago
#3
(Original post by Svesh)
...
\left( \dfrac{1+3x}{1+2x} \right)^2 = (1+3x)^2(1+2x)^{-2}

Expansion of (1+3x)^2 is valid for all x but the expansion of (1+2x)^{-2} isn't.

Overall, the range of validity is where both of these expansions are valid. So if the first one is valid at all times, and the second one isn't, then clearly the problem reduces to finding out when the second expansion is valid.
0
reply
Svesh
Badges: 18
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#4
Report Thread starter 2 years ago
#4
(Original post by RDKGames)
\left( \dfrac{1+3x}{1+2x} \right)^2 = (1+3x)^2(1+2x)^{-2}

Expansion of (1+3x)^2 is valid for all x but the expansion of (1+2x)^{-2} isn't.

Overall, the range of validity is where both of these expansions are valid. So if the first one is valid at all times, and the second one isn't, then clearly the problem reduces to finding out when the second expansion is valid.
Ah ok that makes sense but why is all x valid for (1+3x)^2
0
reply
RDKGames
Badges: 20
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#5
Report 2 years ago
#5
(Original post by Svesh)
Ah ok that makes sense but why is all x valid for (1+3x)^2
Is it not clear? (1+3x)^2 = 9x^2 + 6x + 1 which obviously holds and converges for any x value you put in. It doesn't "break down" for certain x like the infinite expansion.
0
reply
Svesh
Badges: 18
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#6
Report Thread starter 2 years ago
#6
(Original post by RDKGames)
Is it not clear? (1+3x)^2 = 9x^2 + 6x + 1 which obviously holds and converges for any x value you put in. It doesn't "break down" for certain x like the infinite expansion.
oh yh lol completely forgot. Just going back over c4 now and forgotten some knowledge. Thanks!!
1
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Back
to top
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

What is your favourite revision method?

Taking notes manually (53)
21.72%
Note taking apps (6)
2.46%
Flashcards (47)
19.26%
Revision guides (15)
6.15%
Past papers (115)
47.13%
Something else (let us know in the thread) (8)
3.28%

Watched Threads

View All