Alen.m
Badges: 11
Rep:
?
#1
Report Thread starter 5 years ago
#1
Hi guys I've found the binomial expansion of a fraction which i attached here and the whole workings but at the end I'm not sure if the binomial expansion carries on or it should be stopped?i've marked both ways by a question mark so you can see the answers and help me choose one of them.
thanks for your time
Attached files
0
reply
Zacken
Badges: 22
Rep:
?
#2
Report 5 years ago
#2
(Original post by Alen.m)
Hi guys I've found the binomial expansion of a fraction which i attached here and the whole workings but at the end I'm not sure if the binomial expansion carries on or it should be stopped?i've marked both ways by a question mark so you can see the answers and help me choose one of them.
thanks for your time
It definitely carries on. Using the + \cdots \, \, is good practice. In A-Level exams, you'll be asked to "expand up to the term in x^2 or x^3 or whatever" and you can give your final answer without the ellipses.
0
reply
Notnek
  • Study Helper
Badges: 20
Rep:
?
#3
Report 5 years ago
#3
(Original post by Alen.m)
Hi guys I've found the binomial expansion of a fraction which i attached here and the whole workings but at the end I'm not sure if the binomial expansion carries on or it should be stopped?i've marked both ways by a question mark so you can see the answers and help me choose one of them.
thanks for your time
Can you post what the question asks you to do?
0
reply
PLM98
Badges: 6
Rep:
?
#4
Report 5 years ago
#4
Like Zacken says, it carries on forever but you are only asked to do up to a certain term. I always put a +... at the end, it doesn't matter if you don't but it shows that you understand that the expansion carries on.
0
reply
Alen.m
Badges: 11
Rep:
?
#5
Report Thread starter 5 years ago
#5
(Original post by Zacken)
It definitely carries on. Using the + \cdots \, \, is good practice. In A-Level exams, you'll be asked to "expand up to the term in x^2 or x^3 or whatever" and you can give your final answer without the ellipses.
how did you realise that it would carry on?the text book answer is opposite of yours .The question actually asked me to find the binomial expansion of the mentioned fraction on the attachment up to and including the term in x^2
0
reply
Alen.m
Badges: 11
Rep:
?
#6
Report Thread starter 5 years ago
#6
(Original post by PLM98)
Like Zacken says, it carries on forever but you are only asked to do up to a certain term. I always put a +... at the end, it doesn't matter if you don't but it shows that you understand that the expansion carries on.
i know for the negative power it carries on and for positive power it wouldn't carry on but here we have both of multiplied by together so that's why it confuses me
0
reply
Zacken
Badges: 22
Rep:
?
#7
Report 5 years ago
#7
(Original post by Alen.m)
how did you realise that it would carry on?the text book answer is opposite of yours .The question actually asked me to find the binomial expansion of the mentioned fraction on the attachment up to and including the term in x^2
The power series is a sum from n=0/1 to infinity. How is the textbook answer opposite to mine? That's precisely what I said.
0
reply
Zacken
Badges: 22
Rep:
?
#8
Report 5 years ago
#8
(Original post by Alen.m)
i know for the negative power it carries on and for positive power it wouldn't carry on but here we have both of multiplied by together so that's why it confuses me
Well if you have something that doesn't carry on multiplied that does carry on, it's logical to think that the answer would be something that does carry on...
0
reply
Alen.m
Badges: 11
Rep:
?
#9
Report Thread starter 5 years ago
#9
(Original post by Zacken)
Well if you have something that doesn't carry on multiplied that does carry on, it's logical to think that the answer would be something that does carry on...
yeah i agree with you but here's the text book answer if you wanna take a look at it
Attached files
0
reply
Zacken
Badges: 22
Rep:
?
#10
Report 5 years ago
#10
(Original post by Alen.m)
yeah i agree with you but here's the text book answer if you wanna take a look at it
The textbook isn't using = signs. They're throwing away all the terms after the + \cdots and saying that the expansion is \approx what they've written.
0
reply
Alen.m
Badges: 11
Rep:
?
#11
Report Thread starter 5 years ago
#11
(Original post by Zacken)
The textbook isn't using = signs. They're throwing away all the terms after the + \cdots and saying that the expansion is \approx what they've written.
yeah that's what i thought as well but again at the end they use the = sign which i think is incorrect because the expansion carries on
0
reply
Zacken
Badges: 22
Rep:
?
#12
Report 5 years ago
#12
(Original post by Alen.m)
yeah that's what i thought as well but again at the end they use the = sign which i think is incorrect because the expansion carries on
No. They're saying the approximation is equal to that. I could write:

1 \approx 0.5 + 0.4 = 0.9, that means I'm saying that 1 \approx 0.9 even if the last sign is an equals sign. It does not mean I'm saying 1 = 0.9.
0
reply
Alen.m
Badges: 11
Rep:
?
#13
Report Thread starter 5 years ago
#13
(Original post by Zacken)
No. They're saying the approximation is equal to that. I could write:

1 \approx 0.5 + 0.4 = 0.9, that means I'm saying that 1 \approx 0.9 even if the last sign is an equals sign. It does not mean I'm saying 1 = 0.9.
perfectly clear thanks mate
0
reply
PLM98
Badges: 6
Rep:
?
#14
Report 5 years ago
#14
(Original post by Alen.m)
i know for the negative power it carries on and for positive power it wouldn't carry on but here we have both of multiplied by together so that's why it confuses me
If you are multiplying a finite series by an infinite one, yo get an infinite series. Think about it, you are multiplying an infinite number of terms by the finite series all the time, so it never ends.
0
reply
TeeEm
Badges: 19
Rep:
?
#15
Report 5 years ago
#15
too late again ...
0
reply
Notnek
  • Study Helper
Badges: 20
Rep:
?
#16
Report 5 years ago
#16
(Original post by TeeEm)
too late again ...
You were missed.
0
reply
Alen.m
Badges: 11
Rep:
?
#17
Report Thread starter 5 years ago
#17
(Original post by PLM98)
If you are multiplying a finite series by an infinite one, yo get an infinite series. Think about it, you are multiplying an infinite number of terms by the finite series all the time, so it never ends.
it does make sense now thank you
0
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

Do you think receiving Teacher Assessed Grades will impact your future?

I'm worried it will negatively impact me getting into university/college (205)
43.9%
I'm worried that I’m not academically prepared for the next stage in my educational journey (52)
11.13%
I'm worried it will impact my future career (36)
7.71%
I'm worried that my grades will be seen as ‘lesser’ because I didn’t take exams (99)
21.2%
I don’t think that receiving these grades will impact my future (48)
10.28%
I think that receiving these grades will affect me in another way (let us know in the discussion!) (27)
5.78%

Watched Threads

View All
Latest
My Feed