Really tough problem involving sequences...?

Question

What is the limit of the sequence?

3/2, 12/16, 33/54,....

I have been trying to solve this for over 30 minutes & I still can't figure out the pattern. Anyone who can figure this out please tell me how you got your answer. Thanks!

holy...
mcfate are you like a math genius or something

1/2 is correct. i checked it on my graphing calculator

how did you figure out the pattern? did you use any special methods or rules?
(I have a hard test coming up soon...)

Answer 1

The denominators are 2*n^3 (2*1^3 = 2, 2*2^3 = 16, 2*3^3 = 54). Of course, there are any number of third-degree equations which yield 2, 16, 54... but that's almost certainly the simplest.

The numerators are n^3 + 2n (1^3+2*1 = 3, 2^3+2*2 = 12, 3^3+2*3 = 33). Again, there are any number of third-degree equations which yield 3, 12, 33... but that's almost certainly the simplest.

So I would say 1/2, the coefficients of the highest degree of n (n^3) in both the numerator and denominator, divided.

Also, if you check the distance of each term from 1/2, the results are interesting:

3/2 - 1/2 = 1
12/16 - 1/2 = 4/16 = 1/4
33/54 - 1/2 = 6/54 = 1/9

Answer 2

HINT:

What is the difference between 3/2 and 12/16?

What is the difference between 12/16 and 33/54?

What does the word DIFFERENCE mean in math?

Guido