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1. Grade 10 – Mathematics
Quarter I
SUMMATION NOTATION

2. 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

3. Find and evaluate.
෍
𝑘=1
4
5𝑘
= 5( ) + 5( ) + 5( ) + 5( )
= + + +
= 𝟓𝟎
1
5
32 4
10 15 20

4. 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=

5. Find and evaluate.
෍
𝑘=0
4
𝑘2
= ( )2
+( )2
+ ( )2
+( )2
+( )2
= 𝟑𝟎
= + + + +
𝟎 𝟏 𝟐 𝟑 𝟒
𝟎 𝟏 𝟒 𝟗 𝟏𝟔

6. 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

7. 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

8. 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