Sigma notation

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  1. Evaluate the following arithmetic series:
    1. ∑i=110i\sum_{i=1}^{10}i
    2. ∑i=15−3(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=1∞3(−5)i−1\sum_{i=1}^{\infty} 3(-5)^{i-1}
          2. ∑i=1∞−72(−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. 1−2+4−8+...1-2+4-8+...
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        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