Further MathsYears 12–13Further Algebra

Series and summation

Sum series using standard results, method of differences and proof by induction

What you'll learn

  1. 1

    Imagine stacking coins — 1 coin, then 2, then 3, right up to 10. The total number of coins is a series, and adding them up is called summation.

  2. 2

    Build the series 1 + 2 + 3 + 4 by stacking coins in rows.

  3. 3

    Let's sum 1 + 2 + 3 + … + 10 using a clever trick.

  4. 4

    How many pairs do you get when summing 1 to 20?

  5. 5

    Use the number line to sum 2 + 4 + 6 + 8 (the first 4 even numbers).

  6. 6

    Sum the series: 5 + 10 + 15 + 20 (multiples of 5).

  7. 7

    What is the sum of the first 5 odd numbers: 1 + 3 + 5 + 7 + 9?

Practise Series and summation with Whizlo

Free AI-tutored lessons, unlimited practice questions, and progress tracking for ages 16–18. Aligned to the UK National Curriculum.