Sigma notation

All You Need in One Place

Everything you need for Year 6 maths and science through to Year 13 and beyond.

Learn with Confidence

We’ve mastered the national curriculum to help you secure merit and excellence marks.

Unlimited Help

The best tips, tricks, walkthroughs, and practice questions available.

0/11
?
Examples
Lessons
  1. Evaluate the following arithmetic series:
    1. i=110i\sum_{i=1}^{10}i
    2. i=153(i+1)\sum_{i=1}^{5}-3(i+1)
  2. Write the following sum in sigma notation, then evaluate
    7+9+11+13+...+2057+9+11+13+...+205
    1. Evaluate the following geometric series:
      1. i=132(12)i\sum_{i=1}^3 2(\frac{1}{2})^i
      2. i=120(3)i+1\sum_{i=1}^{20} (-3)^{i+1}
    2. Write the following sum in sigma notation, then evaluate
      100+101+1101100-100+10-1+\frac{1}{10}-\frac{1}{100}
      1. Use sigma notation to express S10S_{10} for 5,10,20,40,...-5, 10, -20, 40, ..., then evaluate
        1. Evaluate the following infinite geometric series:
          1. i=13(5)i1\sum_{i=1}^{\infty} 3(-5)^{i-1}
          2. i=172(23)i\sum_{i=1}^{\infty} -\frac{7}{2}(-\frac{2}{3})^i
        2. Write the following sum in sigma notation, then evaluate
          1. 4+2+1+...4+2+1+...
          2. 12+48+...1-2+4-8+...
        Topic Notes
        ?
        Don't you find it tiring when we express a series with many terms using numerous addition and/or subtraction signs? Don't you wish that we have something to symbolise this action? Well we have a solution, introducing the "Sigma Notation"! In this section, we will learn how to utilise the sigma notation to represent a series, as well as how to evaluate it.
        i=1n\sum_{i=1}^n(an equation containing ii)

        \sum : "Sigma"; summation of ithi^{th} term to nthn^{th} term
        ii : index, a counter for the ithi^{th} term
        nn : index of ending term