Question

Express the following sums using sigma notation.

Answer 1

Answer: The given sums in sigma notation are

(a) $\sum_{n=9}^{13}n.$

(b) $\sum_{n=1}^{6}2n.$

(c) $\sum_{n=1}^{4}n^6.$

(d) $\sum_{n=5}^{8}\dfrac{1}{n}.$

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

$S=9+10+11+12+13.$

In sigma notation, the given sum can be written as follows :

$S=\sum_{n=9}^{13}n.$

(b)  2 plus 4 plus 6 plus 8 plus 10 plus 12.

Here, sum is

$S=2+4+6+8+10+12.$

In sigma notation, the given sum can be written as follows :

$S=\sum_{n=1}^{6}2n.$

(c)  1 Superscript 6 Baseline plus 2 Superscript 6 Baseline plus 3 Superscript 6 Baseline plus 4 Superscript 6.

Here, sum is

$S=1^6+2^6+3^6+4^6.$

In sigma notation, the given sum can be written as follows :

$S=\sum_{n=1}^{4}n^6.$

(d) one fifth plus one sixth plus one seventh plus one eighth.

Here, sum is

$S=\dfrac{1}{5}+\dfrac{1}{6}+\dfrac{1}{7}+\dfrac{1}{8}.$

In sigma notation, the given sum can be written as follows :

$S=\sum_{n=5}^{8}\dfrac{1}{n}.$

Thus, the given sums in sigma notation are

(a) $\sum_{n=9}^{13}n.$

(b) $\sum_{n=1}^{6}2n.$

(c) $\sum_{n=1}^{4}n^6.$

(d) $\sum_{n=5}^{8}\dfrac{1}{n}.$

Answer 2

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}.