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Binomial expansion help please! Exam tomorrow!!!

. (a) Find the first 4 terms of the expansion of (1 + x/2)^10 in ascending powers of x, giving each term in its simplest form.
answer is : 1 + 5x + 11.25x^2 + 15x^3

(this is correct according to the mark scheme)

(b) Use your expansion to estimate the value of (1.005)^10, giving your answer to 5 decimal places.
ok, here is where i am confused. i know u need to find a value for x fisrt which is accordding to the ms 0.01 which they got by eqauting (1 + x/2)^10 to (1.005)^10 . but can someone go really slowly through it becuase i dont get 0.01 when i solve for x

? thank so much
right, so you have 1+ x/2 = 1.005 yes? :smile:
So take away 1 from both sides and you have x/2 = 0.005
then times both side by 2 whch gives you x = 0.01

I think this is what you wanted? :tongue:
Original post by starandsmile


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lukas1051
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Original post by starandsmile
. (a) Find the first 4 terms of the expansion of (1 + x/2)^10 in ascending powers of x, giving each term in its simplest form.
answer is : 1 + 5x + 11.25x^2 + 15x^3

(this is correct according to the mark scheme)

(b) Use your expansion to estimate the value of (1.005)^10, giving your answer to 5 decimal places.
ok, here is where i am confused. i know u need to find a value for x fisrt which is accordding to the ms 0.01 which they got by eqauting (1 + x/2)^10 to (1.005)^10 . but can someone go really slowly through it becuase i dont get 0.01 when i solve for x

? thank so much


You know the coefficients when you do (1+x2)10\left (1+\frac{x}{2} \right )^{10} right? And you are trying to figure out (1.005)10(1.005)^{10}

So make (1+x2)=1.005\left (1+\frac{x}{2} \right ) = 1.005

so x2=0.005\frac{x}{2} = 0.005

x=0.01 x = 0.01

Then put the values of xx back into the answer you got for part (a)

Spoiler

(edited 12 years ago)

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