MCR3U
Sigma Notation and Partial Sums
1. Write out the first 3 terms, then evaluate each of the following.
a)
18
12
b)
( 2i 5)
i 1
6
e)
i 0
c)
( 4i 2)
i 0
1
2
i
d)
2k
k 2
9
f)
23
( 3)
11
g)
i
i 1
2k
k 1
h)
2
10
r 0
15
(2 j 10)
j 1
2. Write the following in expanded form (you do not need to evaluate).
a)
4
h 1
d)
10
b)
( h 1) 3
r 1
r
r 5
4
k 0
r 1
6
(r 1)( 1)
r 1
3
e)
x4 k yk
c)
i (i 2)
i
1
3. For each of the following:
i) Identify the series as arithmetic or geometric.
ii) Express in sigma notation.
iii) Evaluate.
1
27
1
9
a) 1 + 3 + 5 + 7 + … + 31
b)
c) 49 + 44 + 29 + …. (to 15 terms)
d) 1 2
e)
1
2
1
3
1
... 27
3
4 8 16 32 ... (to 10 terms)
2
... (to 9 terms)
9
4. More challenging problems. Write the following in sigma notation. You do not need to
evaluate.
a)
1
2
c) x
1
5
3x 2
1
... (to 10 terms)
8
5x 2
....(to 20 terms)
b
1
(1)(2)
d) 1
1
2
1
(2)(3)
1
3
e) (1)(3)(7) + (3)(6)(11) + (5)(9)(15)+ … (to n terms)
1
4
1
1
...
(3)(4)
20(21)
1
... (to 3n terms)
5
MCR3U
5.
If
n
(3k 1)
950 , then find n.
k 1
Answers
1. a) 432 b) –338 c) 550 d) 2046 e) 127/256
+8/9 +9/10 c) 0 - 1 + 2 – 3 + 4 – 5 d) x
16
3. a)
7
(2i 1)
i 1
9
e)
i 1
1 2
2 3
256 b)
i 1
i 1
4
1
(3) i
27
19171
5. 25
13122
3
1
2. a) 8 + 27 +81 +125
f) –14763 g) 24 h) 65384
2
2
x y x y
1093
c)
27
xy
3
y
4
e) 3 + 0 – 1 + 0 + 3
15
20
( 5i 54)
i 1
b) 4/5 + 5/6 +6/7 +7/8
( 2) i
210 d)
i 1
1
341