Sigma notation

Everything You Need in One Place

Homework problems? Exam preparation? Trying to grasp a concept or just brushing up the basics? Our extensive help & practice library have got you covered.

Learn and Practice With Ease

Our proven video lessons ease you through problems quickly, and you get tonnes of friendly practice on questions that trip students up on tests and finals.

Instant and Unlimited Help

Our personalized learning platform enables you to instantly find the exact walkthrough to your specific type of question. Activate unlimited help now!

  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
    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
      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