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Summation Notation

The document covers the concept of summation notation, specifically sigma notation, which provides a concise way to express the sum of a series of terms. Various examples are provided to demonstrate how to evaluate different summations, including both positive and negative series. The notation simplifies the addition of multiple terms by using upper and lower limits along with an index of summation.

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Grade 10 – Mathematics Quarter I SUMMATION NOTATION
SIGMA NOTATION A more concise way to express the sum of 𝑎1 + 𝑎2 + 𝑎3 +…+ 𝑎 𝑛 is to use the summation notation or sigma notation. The Greek letter ∑ (sigma) tells us to sum or add up the terms. ෍ 𝑘 𝑛 3𝑘 end (upper limit) start (lower limit)index of summation substitute
Find and evaluate. ෍ 𝑘=1 4 5𝑘 = 5( ) + 5( ) + 5( ) + 5( ) = + + + = 𝟓𝟎 1 5 32 4 10 15 20
Find and evaluate. ෍ 𝑘=1 6 3𝑘 + 1 = 3( ) + 1 + 3( ) + 1 + 3( ) + 1 + 3 + 1 + 3 + 1 + [3 + 1] = 𝟔𝟗 1 2 3 4 5 6 = +1 + +1 + +1 + +1 + +1 + [ +1]3 6 9 12 15 18 4 + 7 + 10 + 13 + 16 + 19=
Find and evaluate. ෍ 𝑘=0 4 𝑘2 = ( )2 +( )2 + ( )2 +( )2 +( )2 = 𝟑𝟎 = + + + + 𝟎 𝟏 𝟐 𝟑 𝟒 𝟎 𝟏 𝟒 𝟗 𝟏𝟔
Find and evaluate. ෍ 𝑘=1 5 (−1) 𝑘+1 = (−1) +1 +(−1) +1 +(−1) +1 +(−1) +1 +(−1) +1 = (−1) +(−1) +(−1) +(−1) +(−1) = + + + + = 𝟏 𝟏 𝟐 𝟑 𝟒 𝟓 𝟐 𝟑 𝟒 𝟓 𝟔 𝟏 𝟏 𝟏−𝟏 −𝟏
Find and evaluate. ෍ 𝑘=0 3 𝑘3 𝑘 + 1 = ( )3 +1 + ( )3 +1 + ( )3 +1 + ( )3 +1 = + + + = 𝟏𝟏𝟗 𝟏𝟐 𝟎 𝟎 𝟏 𝟏 𝟐 𝟐 𝟑 𝟑 𝟎 𝟏 𝟏 𝟐 𝟖 𝟑 𝟐𝟕 𝟒
Find and evaluate. ෍ 𝑘=1 5 (−1) 𝑘 𝑘 = (−1) + (−1) + (−1) + (−1) + (−1) = − 𝟒𝟕 𝟔𝟎= −1 + 1 2 − 1 3 + 1 4 − 1 5 𝟏 𝟏 𝟐 𝟐 𝟑 𝟑 𝟒 𝟒 𝟓 𝟓 = + + + + −𝟏 𝟏 𝟏 𝟐 −𝟏 𝟑 𝟏 𝟒 −𝟏 𝟓