How Do I Adjust a Formula to Alternate Sequence Terms?

[whatlifeforme]

Homework Statement

I am trying to solve this problem and need help with one aspect.

Homework Equations

sequence: 0,-1,0,1 -- repeated.

The Attempt at a Solution

How do I make every 4th term of the sequence a negative number?

for instance i have: (1 + (-1)^n)/2 but i don't know how to alternative the -1 term in.

 

[SammyS]

Homework Statement

I am trying to solve this problem and need help with one aspect.

Homework Equations

sequence: 0,-1,0,1 -- repeated.

The Attempt at a Solution

How do I make every 4th term of the sequence a negative number?

for instance i have: (1 + (-1)^n)/2 but i don't know how to alternative the -1 term in.

What functions are you willing to use.

This can easily be done with sine or cosine .

You can probably come up with some solution using the "mod" function.

 

[whatlifeforme]

please explain how i would implement cosine or sine.

 

[sudu.ghonge]

Try sin (n*pi/2) and add integer constants to n to shift the series.

 

[whatlifeforme]

then you are going 1, 0, -1, 0. (so if i put sin(pi/2 + npi/2) into the ratio, then i multiply by negative 1 the correct number of times, but what about the zeros? sinx=0 ---> v(sinx) = 0

 

[SammyS]

then you are going 1, 0, -1, 0. (so if i put sin(pi/2 + npi/2) into the ratio, then i multiply by negative 1 the correct number of times, but what about the zeros? sinx=0 ---> v(sinx) = 0

So, it appears you're starting with n = 1 .

Why is it that you say that \displaystyle \ -\,\sin\left(\frac{\pi}{2}+\frac{n\pi}{2}\right)\ doesn't work ?