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1.6.3 Binomial expansion for rational n (A-level only)

Medium
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Question 5

Given that kkk is a constant and the binomial expansion of

1+kx,∣kx∣<1 \sqrt{1 + kx}, \quad |kx| < 1 1+kx​,∣kx∣<1

in ascending powers of xxx up to the term in x3x^3x3 is

1+14x+Ax2+Bx3 1 + \frac{1}{4}x + Ax^2 + Bx^3 1+41​x+Ax2+Bx3
a.

(i) find the value of kkk,

(ii) find the value of the constant AAA and the constant BBB.

[5]
b.

Use the expansion to find an approximate value to 1.2\sqrt{1.2}1.2​.

Show your working and give your answer to 6 decimal places.

[4]

1.6.3 Binomial expansion for rational n (A-level only) Questions

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