Given:
[tex]\sum_{k=3}^{6}(-2 k+5)[/tex]
To find:
The sum of the series.
Solution:
[tex]$\sum_{k=3}^{6}-2 k+5[/tex]
Substitute k = 3, 4, 5 and 6.
[tex]$=[-2 (3)+5] +[ -2 (4) +5]+[-2 (5)+5]+[-2 (6)+5][/tex]
[tex]$=[-6+5] +[ -8 +5]+[-10+5]+[-12+5][/tex]
[tex]$=[-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.
