11/10/04

Some of you may recall the discussion last night at the review session. A student writes, putting a different spin on what we went over last night:

```     We were comparing answers for problem 2 of the old exam.
After realizing our initial answers were wrong and going
through the program a few more time we realized that the
output would always be a perfect square.```

That is true. ...although we did not look at it this way last night.

When I went over the program last night, we agreed the program computes the sum of the odd integers, from 1 to n, where n is the input value.

```     I was wondering whether the answer to the problem (what you
put in under 15 words in the box) should be "outputs perfect squares,"
"A divided by two plus .5 the quantity squared" or "nothing"
(because the information given by the stored value has only vague
resemblance/connection to the initial input value)```

So, what we decided last night was (in not more than 15 words): "given n, the program computes the sum of the odd integers, from one to n."

There is an interesting observation one can make, if one adds the first n integers:

```        1  3  5  7  9
3  3  5  7  9
5  5  5  7  9
7  7  7  7  9
9  9  9  9  9```

Let each digit in the above diagram be counted as "1" and note that 1, 1+3, 1+3+5, 1+3+5+7, ... always forms a perfect square.

```     Personally i believe this program's usefullness is determined by
how a person views its operation.```

I do not understand this comment.

`     I would be grateful if you could clear this up for us.`

Hope the above helps.

Yale Patt

```     Thank you
<< name withheld >>```