+2446 The way I would approach this problem is to find a formula for the sum of consecutive integers 1,2,3,4 ..., n.
Let S = sum of consecutive whole numbers starting with 1
\(S=1+2+3+4+...+n \)
Now, let's reverse the sum. You will see where this is headed in a moment.
\(S= n+(n-1)+(n-2)+(n-3)+...+1\)
Both of the sums above are the same. Now, let's add them together.
| \(S= 1+\hspace{1cm}2\hspace{2mm}+\hspace{1cm}3\hspace{2mm}+\hspace{9mm}4\hspace{2mm}+...+n\\ S=n+(n-1)+(n-2)+(n-3)+...+1\) | Add these sums together. |
| \(2S=\underbrace{(n+1)+(n+1)+(n+1)+...+(n+1)}\\ \hspace{3cm}\text{n occurences of n+1}\) | Knowing that there are n-terms present, we can simplify this slightly. |
| \(2S=n(n+1)\) | Divide by 2 on both sides to figure out the sum of consecutive whole numbers up to n. |
| \(S=\frac{n(n+1)}{2}\) | |
Now that we have generated a formula (a well-known one at that), we can proceed with this problem. I have proved this sum.
We know that the sum must be equal to 666, so let's plug that in and solve.
| \(666=\frac{n(n+1)}{2}\) | Let's eliminate the fraction immediately by multiplying by 2 on both sides. | ||
| \(1332=n(n+1)\) | Expand the right hand side of the equation. | ||
| \(1332=n^2+n\) | Move everything to one side. | ||
| \(n^2+n-1332=0\) | I will tell you beforehand that this quadratic is factorable, but it is pretty difficult to factor, so let's try using the quadratic formula instead. | ||
| \(n=\frac{-1\pm\sqrt{1^2-4(1)(-1332)}}{2(1)}\) | Now, simplify | ||
| \(n=\frac{-1\pm\sqrt{5329}}{2}\) | The radicand happens to be a perfect square. | ||
| \(n=\frac{-1\pm73}{2}\) | Now, solve for both values of n. | ||
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We reject the negative answer because we only care about whole-number solutions, and -37 is not a whole number.
What this means is that \(666=1+2+3+4...+36\), so one must add consecutively 36 positive whole numbers, starting with 1, to get a sum of 666.
+2539 A question of Ethics:
You know, you could just say it's rude to delete your post blab blah etc jabber on and then post back my question right? But no, you didn't.
Oh, But I did. I did that very thing. I said its rude then jabbered on; then posted back your question.
Instead, you acted like ginger. Very bitter, and nasty.
Yes, I did act like Ginger. That’s who I am. Generally, it’s only adolescents and adults who act like little bratty children that of think of me as bitter and nasty. So, it’s easy to understand why you think so.
What you're telling me, is that if CPhill or Melody weren't going to hide unethical comments as such, why would you want to make them in the first place?
Your question is a non sequitur. I’ll answer it, though.
It’s not unethical to sound a fire alarm if there is a fire. It’s not unethical to sound the Ahole alarm if there is an Ahole nearby.
However, it is unethical to vandalize a post. Once you make a post and it is answered, it’s no longer your post—it belongs to the forum. Over time, potentially thousands of students can learn from these posts. However, that can never happen, because you effectively destroy them. That is unethical and it is petty; so yes, I would curse you. The only reason I didn’t, is because a moderator would likely hide the post and you would not be able to read it. That would be kind of pointless, wouldn’t it?
Another thing you should know is Andree Massow, the web master, will ban you for deleting your question posts. He has no sense of humor about it. . . . Well maybe he does have a sense of humor about it, but he will still banish you. Here’s an example of someone who píssed off Herr Massow.
Bad character I suppose. I would try to start acting like Fanta, very nice and sweet.
Scréw that! That’s out of character for me. Perhaps my character is bad. It’s not a certainty, but it’s open for debate. Irish GinerAle doesn’t rank high on the list of favorite sodas for bratty children and adolescents, but it’s higher on the list than the lime-y flavor of Julius.
GingerAle isn’t just a sobriquet— it is my name. I’m Ginger Alexandra.
GA
