Question

Which of the following expressions correctly uses the properties of summations to represent

Answer 1

Option C is correct.

`7 \cdot \sum_(i=1)^(18) i^2 + 9 \cdot 18`

Explanation:

Given the expression:
`\sum_(i=1)^(18) (7i^2+9)`

Using properties of summation:

• 
  `\sum_(i=1)^(n) (a+bi) =\sum_(i=1)^(n) a + \sum_(i=1)^(n) bi`

• 
  `\sum_(i=1)^(n) a = an`

Using properties of summation in the given expression we have;

`\sum_(i=1)^(18) (7i^2+9)`

=
`\sum_(i=1)^(18) 7i^2 + \sum_(i=1)^(18) 9`

=
`7 \cdot \sum_(i=1)^(18) i^2 + 9 \cdot 18`

Therefore, the following given expression uses the properties of summation to represents is,
`7 \cdot \sum_(i=1)^(18) i^2 + 9 \cdot 18`