**QUESTION**

1.Calculate each of the following:

1^{3} + 5^{3} + 3^{3} =
??

16^{3} + 50^{3} +
33^{3} = ??

166^{3} + 500^{3} +
333^{3} = ??

1666^{3} + 5000^{3} +
3333^{3} = ??

What do you see? Can you state and prove a generalization of your observations?

2. The sequence (x_{n}) of positive real numbers
satisfies the relationship
x_{n-1}x_{n}x_{n+1} = 1 for all n >
2. If x_{1 }= 1 and x_{2} = 2, what are
the values of the next few terms? What can you say about the
sequence? What happens for other starting values? The sequence
(y_{n}) satisfies the relationship
y_{n-1}y_{n+1} + y_{n} = 1 for
all n > 2. If y_{1} = 1 and y_{2} = 2,
what are the values of the next few terms? What can you say about
the sequence? What happens for other starting values?