Question

What is the sum of the series? Write in expanded form making sure to show all steps used to find the sum.

Answer 1

Given:

`$\sum_(k=3)^(6)(-2 k+5)`

To find:

The sum of the series.

Solution:

`$\sum_(k=3)^(6)(-2 k+5)`

Substitute k = 3.

`-2 (3)+5=-6+5=-1`

Substitute k = 4.

`-2 (4)+5=-8+5=-3`

Substitute k = 5.

`-2 (5)+5=-10+5=-5`

Substitute k = 6.

`-2 (6)+5=-12+5=-7`

`$\sum_(k=3)^(6)(-2 k+5)=(-1)+(-3)+(-5)+(-7)`

Apply minus plus rule:
`+(-a)=-a`

`=-1-3-5-7`

`=-16`

`$\sum_(k=3)^(6)-2 k+5=-16`

Therefore the sum of the series is -16.