Question 1
1 markWhich of the following is the correct expression for the sum of the finite series \(\sum_{r=1}^n (4r - 3)\)?
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 2
1 markWhich of the following expressions is equivalent to the sum of the finite series \(\sum_{r=1}^n r^2(r+2)\)?
Question 3
2 marksUsing 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 marksEvaluate 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 marksShow 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 marksGiven 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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