Given:
[tex]$\sum_{k=3}^{6}(-2 k+5)[/tex]
To find:
The sum of the series.
Solution:
[tex]$\sum_{k=3}^{6}(-2 k+5)[/tex]
Substitute k = 3.
[tex]-2 (3)+5=-6+5=-1[/tex]
Substitute k = 4.
[tex]-2 (4)+5=-8+5=-3[/tex]
Substitute k = 5.
[tex]-2 (5)+5=-10+5=-5[/tex]
Substitute k = 6.
[tex]-2 (6)+5=-12+5=-7[/tex]
[tex]$\sum_{k=3}^{6}(-2 k+5)=(-1)+(-3)+(-5)+(-7)[/tex]
Apply minus plus rule: [tex]+(-a)=-a[/tex]
[tex]=-1-3-5-7[/tex]
[tex]=-16[/tex]
[tex]$\sum_{k=3}^{6}-2 k+5=-16[/tex]
Therefore the sum of the series is -16.
