I'm trying to create a formula for this sequence and just can't figure it out:
{ 1/1, 1/3, 1/2, 1/4, 1/3, 1/5, 1/4, 1/6, ... }
Any ideas?
Hello, mxrider530!
This is a wicked problem!
I examined the denominators,Find a formula for this sequence: .
. .
I considered the denominators for odd and for even
. . If is odd, add 1 and divide by 2: . .[1]
. . If is even, divide by 2 and add 2: . .[2]
How can we alternate between the two formulas: .[1] and [2] ?
. . Multiply [1] by: . multiply [2] by: . and add the results.
We have: .
. . This simplifies to: .
. . Therefore: .