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, 4, 5 and 6.

`$=[-2 (3)+5] +[ -2 (4) +5]+[-2 (5)+5]+[-2 (6)+5]`

`$=[-6+5] +[ -8 +5]+[-10+5]+[-12+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.