Question

write the sum without sigma notation. then evaluate.

sum _ { k = 2 } ^ { 6 } cos k pi

write out the sum.

sum _ { k = 2 } ^ { 6 } cos k pi =

Explanation:

Step1: Substitute \(k = 2\)

When \(k = 2\), \(\cos(2\pi)=1\)

Step2: Substitute \(k = 3\)

When \(k = 3\), \(\cos(3\pi)=-1\)

Step3: Substitute \(k = 4\)

When \(k = 4\), \(\cos(4\pi)=1\)

Step4: Substitute \(k = 5\)

When \(k = 5\), \(\cos(5\pi)=-1\)

Step5: Substitute \(k = 6\)

When \(k = 6\), \(\cos(6\pi)=1\)

The sum \(\sum_{k = 2}^{6}\cos(k\pi)=\cos(2\pi)+\cos(3\pi)+\cos(4\pi)+\cos(5\pi)+\cos(6\pi)\)

$$
LATEXBLOCK0
$$

Answer:

\(1\)