Date: Tue, 25 Feb 1997 13:14:08 -0600 (CST)

Name: Karyn
Level: Middle

Question:

Josie says that

```s= __n__ and __s__ =n
n+1       1-s
```

are two ways to write the same formula. Describe whether or not you agree with Joise. Explain how you made your decision.

Thankyou very much
Karyn

Hi Karyn

I think the place to start is: test it to see if you blieve it: Try n=1. Then s= 1/2. Does that fit the other equation? Now try s= 2 in the second equation. Then n= -1. Does that pair s=2, n=-1 fit the first equation?

Finally, you can do the same thing with the proposed letter answers: If you put (n)/(n-1) in for s in the second equation, does it simplify to be equal? (and Vice versa?)

That MAY not be what your teacher expects. She may suggest you 'simplify and solve'. Are these two approaches equally good?

The "simplify and solve" method would go as follows:

```multiply both sides of  s=__n__ by n+1 to get s(n+1)=n.
n+1
```

Now expand to sn+s=n.

Subtract sn from both sides to get s=n-sn or s=n(1-s).

If you now divide both sides by (1-s) you get Josie's second expression.

Is this last step always valid? Is there any value of s for which division by 1-s is not valid?

Cheers
Walter and Penny

Go to Math Central