# Question on binomial theorem

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#1
Question:
Find the first four terms of the expansion of in ascending of x. Substitute and obtain the value of correct to five significant figures

a) find the first four terms of the expansion of in ascending of x.

b)Substitute and obtain the value of correct to five significant figures
I have problem with this part

now it says to sub
so;

using the expansion;

i sub x = 1/00 into the expansion

it produces 0.959168
i know that

My issue is that I dont know why I am not getting 4.795831523
since part b is a simple substitution question asking me to sub x = 1/100 shouldn't the I get the answer 4.795831523, when i sub x= 1/100 into the expansion or binomial.

thank you for helping me
Last edited by bigmansouf; 1 year ago
0
1 year ago
#2
X = 1/100 does not produce sqrt(23) for
(1 - 8x)^0.5
Just sub in the value?

How can you transform
(1 - 8/100)^0.5
Into sqrt(23)?
(Original post by bigmansouf)
Question:
Find the first four terms of the expansion of in ascending of x. Substitute and obtain the value of correct to five significant figures

a) find the first four terms of the expansion of in ascending of x.

b)Substitute and obtain the value of correct to five significant figures
I have problem with this part

now it says to sub
so;

using the expansion;

i sub x = 1/00 into the expansion

it produces 0.959168
i know that

My issue is that I dont know why I am not getting 4.795831523
since part b is a simple substitution question asking me to sub x = 1/100 shouldn't the I get the answer 4.795831523, when i sub x= 1/100 into the expansion or binomial.

thank you for helping me
Last edited by mqb2766; 1 year ago
0
1 year ago
#3
(Original post by bigmansouf)
Question:
Find the first four terms of the expansion of in ascending of x. Substitute and obtain the value of correct to five significant figures

a) find the first four terms of the expansion of in ascending of x.

b)Substitute and obtain the value of correct to five significant figures
I have problem with this part

now it says to sub
so;

using the expansion;

i sub x = 1/00 into the expansion

it produces 0.959168
i know that

My issue is that I dont know why I am not getting 4.795831523
since part b is a simple substitution question asking me to sub x = 1/100 shouldn't the I get the answer 4.795831523, when i sub x= 1/100 into the expansion or binomial.

thank you for helping me
You can only have worked out the value of the LHS when x = 1/100 with a calculator. This defeats the object of the question - the idea of binomial approximations in this context is to find the approximate value of roots by using only addition and multiplication of rational numbers.

When you substitute x = 1/100 into the LHS, you get (1 - 8/100)^0.5 = (1 - 2/25)^0.5 = (23/25)^0.5. Does that give you any ideas?
0
#4
(Original post by mqb2766)
X = 1/100 does not produce sqrt(23) for
(1 - 8x)^0.5
Just sub in the value?

Can you transform
(1 - 8/100)^0.5
Into sqrt(23)?
yes i can i get
i see now i thought that binomial theorem can be used to find approx but this question is not asking me the approximate to the square roof of 23
i thought that it was an approximate type of question. I personally do not see the point of part b and what it is trying to teach me
0
1 year ago
#5
(Original post by bigmansouf)
yes i can i get
i see now i thought that binomial theorem can be used to find approx but this question is not asking me the approximate to the square roof of 23
i thought that it was an approximate type of question. I personally do not see the point of part b and what it is trying to teach me
It is asking for an approximation to root 23. Keep going. Split up the (23/25)^0.5.
0
1 year ago
#6
So multiply the answer you got by 5.
(Original post by bigmansouf)
yes i can i get
i see now i thought that binomial theorem can be used to find approx but this question is not asking me the approximate to the square roof of 23
i thought that it was an approximate type of question. I personally do not see the point of part b and what it is trying to teach me
0
#7
(Original post by Pangol)
You can only have worked out the value of the LHS when x = 1/100 with a calculator. This defeats the object of the question - the idea of binomial approximations in this context is to find the approximate value of roots by using only addition and multiplication of rational numbers.

When you substitute x = 1/100 into the LHS, you get (1 - 8/100)^0.5 = (1 - 2/25)^0.5 = (23/25)^0.5. Does that give you any ideas?
can be changed to

then to transfer to by multiplying by 5

thus;

1
#8
i get it now
thanks
0
1 year ago
#9
(Original post by bigmansouf)
can be changed to

then to transfer to by multiplying by 5

thus;

That's it - so it is an approximation question!
1
1 year ago
#10
One thing its trying to teach you is that while the expansion is only valid for
|x|<1/8
So for sqrt of 0 to 2 .
You can use transformations to apply it to other numbers outside this range.
(Original post by bigmansouf)
yes i can i get
i see now i thought that binomial theorem can be used to find approx but this question is not asking me the approximate to the square roof of 23
i thought that it was an approximate type of question. I personally do not see the point of part b and what it is trying to teach me
Last edited by mqb2766; 1 year ago
0
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