Question bank1.7 D: Sequences and series

1.7 D: Sequences and series

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Question 32

Use binomial expansions to show that

$1+5x1−x≈1+3x−32x2\displaystyle \sqrt{\frac{1 + 5x}{1 - x}} \approx 1 + 3x - \frac{3}{2}x^2$

for small values of $x$ .

[4]

A student substitutes $x=12\displaystyle x = \frac{1}{2}$ into the expansion to find an estimate for $7\sqrt{7}$ . Give a reason why the student should not use $x=12\displaystyle x = \frac{1}{2}$ .

[1]

Substitute $x=19\displaystyle x = \frac{1}{9}$ into $1+5x1−x≈1+3x−32x2\displaystyle \sqrt{\dfrac{1 + 5x}{1 - x}} \approx 1 + 3x - \frac{3}{2}x^2$ to obtain an approximation for $7\sqrt{7}$ . Give your answer as a fraction in its simplest form.

[2]

Use binomial expansions to show that

$1+5x1−x≈1+3x−32x2\displaystyle \sqrt{\frac{1 + 5x}{1 - x}} \approx 1 + 3x - \frac{3}{2}x^2$

for small values of $x$ .

A student substitutes $x=12\displaystyle x = \frac{1}{2}$ into the expansion to find an estimate for $7\sqrt{7}$ . Give a reason why the student should not use $x=12\displaystyle x = \frac{1}{2}$ .

[1]

[2]

1.7 D: Sequences and series

Question 32

Markscheme

1.7 D: Sequences and series

Question 32

Markscheme

1.7 D: Sequences and series

Question 32

1.7 D: Sequences and series Questions

1.7 D: Sequences and series

Question 32

1.7 D: Sequences and series Questions