Answer: The given sums in sigma notation are
(a) [tex]\sum_{n=9}^{13}n.[/tex]
(b) [tex]\sum_{n=1}^{6}2n.[/tex]
(c) [tex]\sum_{n=1}^{4}n^6.[/tex]
(d) [tex]\sum_{n=5}^{8}\dfrac{1}{n}.[/tex]
Step-by-step explanation: We are given to express the following sums using sigma notation.
(a) 9 plus 10 plus 11 plus 12 plus 13.
Here, sum is
[tex]S=9+10+11+12+13.[/tex]
In sigma notation, the given sum can be written as follows :
[tex]S=\sum_{n=9}^{13}n.[/tex]
(b) 2 plus 4 plus 6 plus 8 plus 10 plus 12.
Here, sum is
[tex]S=2+4+6+8+10+12.[/tex]
In sigma notation, the given sum can be written as follows :
[tex]S=\sum_{n=1}^{6}2n.[/tex]
(c) 1 Superscript 6 Baseline plus 2 Superscript 6 Baseline plus 3 Superscript 6 Baseline plus 4 Superscript 6.
Here, sum is
[tex]S=1^6+2^6+3^6+4^6.[/tex]
In sigma notation, the given sum can be written as follows :
[tex]S=\sum_{n=1}^{4}n^6.[/tex]
(d) one fifth plus one sixth plus one seventh plus one eighth.
Here, sum is
[tex]S=\dfrac{1}{5}+\dfrac{1}{6}+\dfrac{1}{7}+\dfrac{1}{8}.[/tex]
In sigma notation, the given sum can be written as follows :
[tex]S=\sum_{n=5}^{8}\dfrac{1}{n}.[/tex]
Thus, the given sums in sigma notation are
(a) [tex]\sum_{n=9}^{13}n.[/tex]
(b) [tex]\sum_{n=1}^{6}2n.[/tex]
(c) [tex]\sum_{n=1}^{4}n^6.[/tex]
(d) [tex]\sum_{n=5}^{8}\dfrac{1}{n}.[/tex]
The answer is:
(a) \sum_{n=9}^{13}n.
(b) \sum_{n=1}^{6}2n.
(c) \sum_{n=1}^{4}n^6.
(d) \sum_{n=5}^{8}\dfrac{1}{n}.
