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Series — WFM01 IAL Further Mathematics practice questions · Study-IAL

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Further Mathematics
WFM01
1.7

Series

WFM01Topic 1.72 questions

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Summing series using standard results for $\sum r$ , $\sum r^2$ and $\sum r^3$ .

Previous topic1.6Transformations using matrices Next topic 1.8Proof by induction

3

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Questions

Multiple choice: 1
Calculation: 1
Total: 2

Sample questions

Original practice questions written in the style of the exam.

Question 16 marks
(a) Use the standard results for $\sum r$ and $\sum r^2$ to show that $\sum_{r=1}^{n} r(r + 2) = \frac{1}{6}n(n + 1)(2n + 7)$

(b) Hence find the value of $\displaystyle\sum_{r=11}^{20} r(r + 2)$ .
Mark scheme
- M1 Expands to $\sum r^2 + 2\sum r$ (1)
- M1 Substitutes $\tfrac{1}{6}n(n+1)(2n+1) + n(n+1)$ (1)

n

+

1)(2n+

7)

61

n

(

n

+

1)(2n+

1)+

n(n+

1)

M1 Takes out the factor

\tfrac{1}{6}n(n+1)

(1)

A1

\tfrac{1}{6}n(n+1)(2n + 1 + 6) = \tfrac{1}{6}n(n+1)(2n+7)

(1)

M1 Uses

f(20) - f(10)

(1)

A1

3290 - 495 = 2795

(1)