Question

Express the following sums using sigma notation.

a. 9 plus 10 plus 11 plus 12 plus 13
b. 2 plus 4 plus 6 plus 8 plus 10 plus 12
c. 1 Superscript 6 Baseline plus 2 Superscript 6 Baseline plus 3 Superscript 6 Baseline plus 4 Superscript 6
d. one fifth plus one sixth plus one seventh plus one eighth

Answer 1

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}.

Answer 2

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)(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=(1)/(5)+(1)/(6)+(1)/(7)+(1)/(8).`

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

`S=\sum_(n=5)^(8)(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)(1)/(n).`