AS maths question c2?

St. Jimmy @St. Jimmy

May 2021 3 70 Report

AS maths question c2?

Expand (1 + 3x)^8 in ascending powers of x up to and including the term in x3.

You should simplify each coefficient in your expansion.

i am pretty sure the answer to this is 1 + 24x + 252x^2 + 1512x^3

(b) Use your series, together with a suitable value of x which you should state, to

estimate the value of (1.003)^8, giving your answer to 8 significant figures.

i have absolutly no idea how to even begin doing part b. please help

thanks

Science & Mathematics / Mathematics

Verified answer

(a)

(1 + 3x)^8 = 1 + 8(3x) + (8*7/2) (3x)^2 + (8*7*6/6) (3x)^3 + ...

= 1 + 24x + 252x^2 + 1512x^3 + ...

You are correct so far, well done

(b)

(1.003)^8 = (1 + 3x)^8

when

1.003 = 1 + 3x

3x = 0.003

x = 0.001

Now just substitute this into your expansion from (a)

1 + 24x + 252x^2 + 1512x^3 = 1 + 24 [0.001] + 252 [0.001]^2 + 1512 [0.001]^3

= 1 + 0.024 + 0.000252 + 0.000001512

= 1.024253512

Hence

(1.003)^8 = 1.0242535 to 8 significant figures

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