Sigma notation

Sigma notation

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.

Lessons

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
  • 1.
    Evaluate the following arithmetic series:
    a)
    i=110i\sum_{i=1}^{10}i

    b)
    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

  • 3.
    Evaluate the following geometric series:
    a)
    i=132(12)i\sum_{i=1}^3 2(\frac{1}{2})^i

    b)
    i=120(3)i+1\sum_{i=1}^{20} (-3)^{i+1}


  • 4.
    Write the following sum in sigma notation, then evaluate
    100+101+1101100-100+10-1+\frac{1}{10}-\frac{1}{100}

  • 5.
    Use sigma notation to express S10S_{10} for 5,10,20,40,...-5, 10, -20, 40, ..., then evaluate

  • 6.
    Evaluate the following infinite geometric series:
    a)
    i=13(5)i1\sum_{i=1}^{\infty} 3(-5)^{i-1}

    b)
    i=172(23)i\sum_{i=1}^{\infty} -\frac{7}{2}(-\frac{2}{3})^i


  • 7.
    Write the following sum in sigma notation, then evaluate
    a)
    4+2+1+...4+2+1+...

    b)
    12+48+...1-2+4-8+...