Pearson Edexcel International A Level · Further Mathematics (YFM01)

Series: Practice Questions

2 multiple-choice questions marked as you go, and 4 written questions with worked solutions. All on Series.

6 questions16 marksFree, no account
Question 1
1 mark

Which of the following is the correct expression for the sum of the finite series \(\sum_{r=1}^n (4r - 3)\)?

Question 2
1 mark

Which of the following expressions is equivalent to the sum of the finite series \(\sum_{r=1}^n r^2(r+2)\)?

Question 3
2 marks

Using the standard result for \( \sum_{r=1}^n r \), state the value of \( \sum_{r=1}^{50} r \).

Write your answer out first, then check it against the worked solution.

Question 4
4 marks

Evaluate the finite series \( \sum_{r=1}^{10} (r^2 + 1) \) using standard summation formulae.

Write your answer out first, then check it against the worked solution.

Question 5
5 marks

Show that the sum of the series \( \sum_{r=1}^n (r^2 - r) \) can be expressed in the form \( \frac{1}{3}n(n+1)(n-1) \).

Write your answer out first, then check it against the worked solution.

Question 6
3 marks

Given that \(\sum_{r=1}^{n} r = \frac{1}{2}n(n+1)\) and \(\sum_{r=1}^{n} r^2 = \frac{1}{6}n(n+1)(2n+1)\),
(a) Show that \(\sum_{r=1}^{n} (r^2 - r) = \frac{1}{3}n(n+1)(n-1)\).
(b) Hence, evaluate \(\sum_{r=10}^{20} (r^2 - r)\).

Write your answer out first, then check it against the worked solution.

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