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C2 Help?!

in the expansion of (1+x/2)^n in ascending powers of x the coefficient of x^2 is 30.
a) find n
b) find the first four terms of the expansion

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Kevin De Bruyne

Original post by ramshahk

in the expansion of (1+x/2)^n in ascending powers of x the coefficient of x^2 is 30.
a) find n
b) find the first four terms of the expansion

What is the coefficient of x^2 in terms of n in the expansion?

OP

Original post by SeanFM

What is the coefficient of x^2 in terms of n in the expansion?

30

Kevin De Bruyne

Original post by ramshahk

30

As I specified in my post - in terms of n?

Or, what are the first 3 terms in the expansion of (1+(x/2))^n?

Study Forum Helper

Original post by ramshahk

in the expansion of (1+x/2)^n in ascending powers of x the coefficient of x^2 is 30.
a) find n
b) find the first four terms of the expansion

Can I encourage you to post A level maths questions in F38 (the Maths Forum)?

Could you use the formula in your formula book to write down the

x^2

term in the expansion?

OP

Original post by Mr M

Can I encourage you to post A level maths questions in F38 (the Maths Forum)?

Could you use the formula in your formula book to write down the

x^2

term in the expansion?

i have tried but it doesnt work

Study Forum Helper

Original post by ramshahk

i have tried but it doesnt work

Really? Can you post your working? A photo will do (assuming it is the right way up).

OP

Original post by Mr M

Really? Can you post your working? A photo will do (assuming it is the right way up).

sorry i threw the working out in the bin ahaha

OP

Original post by ramshahk

sorry i threw the working out in the bin ahaha

i dont know how to use the formula with this question

Study Forum Helper

Original post by ramshahk

i dont know how to use the formula with this question

Ok I'll start you off.

(1+\frac{x}{2})^n = 1 + n(\frac{x}{2})+\frac{n(n-1)}{2!}(\frac{x}{2})^2 +...

You'll need to do some simplification and add a fourth term.

(edited 7 years ago)

OP

Original post by Mr M

Ok I'll start you off.

(1+\frac{x}{2})^n = 1 + n(\frac{x}{2})+\frac{n(n-1)}{2!}(\frac{x}{2})^2 +...

You'll need to do some simplification and add a fourth term.

yeah what do you do after that

Study Forum Helper

Original post by ramshahk

yeah what do you do after that

Use the fact that the coefficient of

x^2=30

. You'll need to form and solve a quadratic to find the value of

n

.

OP

Original post by Mr M

Use the fact that the coefficient of

x^2=30

. You'll need to form and solve a quadratic to find the value of

n

.

??

Study Forum Helper

Original post by ramshahk

??

I'm getting the impression this is too difficult for you at the moment. Could you ask your teacher to explain it to you tomorrow?

OP

Original post by Mr M

I'm getting the impression this is too difficult for you at the moment. Could you ask your teacher to explain it to you tomorrow?

haha okay will do

TheConfusedMedic

@ramshahk Mr M has told you how to find the coefficient of x^2 algebraically (in terms of n).
You know that this is equal to 30 so can you form an equation with these two pieces of information in order to solve n?

(edited 7 years ago)

OP

Original post by surina16

@ramshahk Mr M has told you how to find the coefficient of x^2 algebraically (in terms of n).
You know that this is equal to 30 so can you form an equation with these two pieces of information in order to solve n?

yeah i get that bit

TheConfusedMedic

Original post by ramshahk

yeah i get that bit

Great, so what did you get for n?

OP

Original post by surina16

Great, so what did you get for n?

i didnt find out n

Study Forum Helper

Original post by ramshahk

i didnt find out n

Mr M has given you the first few terms of the expansion. See that term with 3rd term

(\frac{x}{2})^2

?? Rewrite it as

A \cdot x^2

where A is a function of

n

and make it equal to 30. Then solve for n.

(edited 7 years ago)

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