How Is the Sequence 2, 0, 2/27, 0, 2/125 Formulated?

[Alexx1]

Can someone help me with this sequence?

2 0 2/27 0 2/125

If I only look at the odd numbers it's: 2/n^3

But I don't know how they get that zero..

 

[CRGreathouse]

Could be just every other term is 0.

A convenient way to write that would be 1 - (-1)^n in place of the 2.

 

[Alexx1]

Could be just every other term is 0.

A convenient way to write that would be 1 - (-1)^n in place of the 2.

Thank you very much!

 

[Alexx1]

Could be just every other term is 0.

A convenient way to write that would be 1 - (-1)^n in place of the 2.

Can you help me with this sequence also?

1 4 1 16 1 36

If I only look at the odd numbers it's: n^2

But I don't know how they get to '1'..

 

[CRGreathouse]

Can you help me with this sequence also?

1 4 1 16 1 36

If I only look at the odd numbers it's: n^2

But I don't know how they get to '1'..

Again, just define it that way: f(2n + 1) = 1, f(2n) = 4n^2. You can use the same trick with (-1)^n if you want -- make the exponent 0 for odds and 1 for evens.

 

[Alexx1]

Again, just define it that way: f(2n + 1) = 1, f(2n) = 4n^2. You can use the same trick with (-1)^n if you want -- make the exponent 0 for odds and 1 for evens.

How do you define f(n)?

 

[HallsofIvy]

He just did. If n is odd, n= 2m+ 1 for some integer m so f(n)= 1, if n is even, n= 2m for some integer m so f(n)= f(2m)= 4(m)^2. Of course, if n= 2m then m= n/2 so you could also write this as 4(n/2)^2= 4n^2/4= n^2.