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The thing i messaged you doesn't work...

I don't know what the site would do without a person like Melody. Thank you for your constant support!

Precisely.

The answer is $${\mathtt{\,-\,}}{\frac{{\mathtt{1}}}{{\mathtt{12}}}}$$; it can seem strange, because it's a negative number, and it's not an integer; but that result is absolutely true.

Here's your cookie:

There's the proof I usually use:

$$\\S_1=1-1+1-1+1-1+...
\\S_2=1-2+3-4+5-6+...
\\S=1+2+3+4+5+6+...
\\\\S_1=1-1+1-1+1-1+...
\\1-S_1=1-(1-1+1-1+1-...)=1-1+1-1+1-1+...=S_1
\\1=2S_1
\\S_1=\frac{1}{2}$$

$$\\\\S_2=1-2+3-4+5-6+...
\\S_2+S_1=(1-2+3-4+5-6+...)+(1-1+1-1+1-1+...)
\\S_2+S_1=2-3+4-5+6-7+...
\\-1+S_1+S_2=-1+(2-3+4-5+6-7+...)=-1+2-3+4-5+6-7+...=-S_2
\\-1+\frac{1}{2}=-2S_2
\\-2S_2=-\frac{1}{2}
\\S_2=\frac{-\frac{1}{2}}{-2}=\frac{1}{4}$$

$$\\\\S=1+2+3+4+5+6+...
\\S-S_2=(1+2+3+4+5+6+...)-(1-2+3-4+5-6+...)=4+8+12+16+20+24...
\\=4(1+2+3+4+5+6+...)=4S
\\-S_2=3S
\\-\frac{1}{4}=3S
\\S=-\frac{-\frac{1}{4}}{3}=-\frac{1}{12}$$

These are the times I came up with by equating the two functions, littlehand and bighand, that I used to generate the graph in yesterday's problem.  They are in hour-minute-second format on a 24-hour clock.

How do these times compare with yours civonamzuk?

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Greetings, Your Majesty:

 The anniversary of Sir CPhill’s knighthood  be the tenth this inst. I remember this well, for it be during a time when ye were considering lobbing off mine head for insolence.

Yea, Sir CPhill, whom His Majesty hath just Knighted, stood as a guard to the chambers of the Knights and did witness the circular pun and the leads to a circular paradox by Sir Cumference.

The answer is actually $${\mathtt{\,-\,}}{\frac{{\mathtt{1}}}{{\mathtt{12}}}}$$

Let:

S=1+2+3+4+5+6+7+8+9+n

We know the answer to the following infinite sum:

S₂=1-1+1-1+1-1+1-1+1-1+1-1+1-....=$${\frac{{\mathtt{1}}}{{\mathtt{2}}}}$$

We can therefore solve for this sum:

S₃=1-2+3-4+5-6+7-8+9-....

We add them:

S_{3=      1-2+3-4+5-6+7-8...}

S₃=       _{+1-2+3-4+5-6+7-8...}

         ________________

2S_{3=    1-1+1-1+1-1+1-1+1-....}

Therefore:

2S₃=S₂=$${\frac{{\mathtt{1}}}{{\mathtt{2}}}}$$

S₃=$${\frac{{\mathtt{1}}}{{\mathtt{4}}}}$$

We can subtract S₃ from S:

S-S₃=  1+2+3+4+5+6+7+8+9-...

         -[1- 2+3- 4+5- 6+7- 8+9-...

       _________________________

               4   +  8  +  12  +  16   +....

If we take a factor of 4 out:

S-S₃=4(1+2+3+4+5+6+7+8+9+...)

The sum inside the parentheses is S:

S-S₃=4(S)

We know S₃=$${\frac{{\mathtt{1}}}{{\mathtt{4}}}}$$

S-$${\frac{{\mathtt{1}}}{{\mathtt{4}}}}$$=4(S)

Subtract S from each side:

$${\mathtt{\,-\,}}{\frac{{\mathtt{1}}}{{\mathtt{4}}}}$$=3S

Divide by 3:

$${\mathtt{\,-\,}}{\frac{{\mathtt{1}}}{{\mathtt{12}}}}$$=S

∞

∑ n+1=$${\mathtt{\,-\,}}{\frac{{\mathtt{1}}}{{\mathtt{12}}}}$$

n

-Daedalus

No it wasn't that quick.  Have a look through the old wraps and see if you can find a date for us MG.

Then I'll put it in with the other important anniverary dates  :))

$${\frac{{\mathtt{70}}{\mathtt{\,\times\,}}{\mathtt{5\,280}}}{{\mathtt{3\,600}}}} = {\frac{{\mathtt{308}}}{{\mathtt{3}}}} = {\mathtt{102.666\: \!666\: \!666\: \!666\: \!666\: \!7}}$$

Yes he is!

I think Nauseated is already out!

He did win the battle (in the post) but then Titanium's army cornered him...But he should be out, after all isn't he the best at trashtalk :)

Ok we surrender. I am not sure what that means because we are still in charge.

Thanks Titanium Soldier, that is great if you really mean it :)

The forum can be fun for everyone who likes mathematics and likes to learn.  

But it is definitely not facebook or a war game site.  

Please can we have Nauseated back.  We keep him muzzled but he doesn't like cold damp dungeons.

This is his bed he shares it with his best friend Suzie.  Look how sad she is.  She is really missing him.  

@Darkblaze thanks for the method. But answer,...??.

Lol

$${\mathtt{256\,000}}{\mathtt{\,\times\,}}{\mathtt{0.02}} = {\mathtt{5\,120}}$$

Woah!!!

So CPhill you joined last year March 13th .  And the next day you became a Mod?

So lucky.

I would love to be a Mod but i haven't got the knowledge yet (because all the mods are people who always answer questions and are good. Or is it maturity)

Without knowing the value of c the most general approach is to use the quadratic formula.

First rewrite as   x² + 11x + 12-9c = 0 and then solve as:

x =  ( -11 ± √[121 - 4(12-9c)] )/2  or x = ( -11 ± √[73 + 36c] )/2

Once you have a value for c you can plug it in the expression above to get numerical values for x.  Note that if c is a number less than -73/36 the resulting values of x will be complex.

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2% is 0.02, so take 256,000 times 0.02 to get the answer.

OK, but this works only for a finite amount of numbers; now, there are infinitely many numbers from 1 to infinity.

But the correct answer is not infinity; it's a real number. And it's just astounding, I think.

5280 feet= 1 mile.

3600 seconds=1 hour.

70*5280/3600 would be how many feet the car travels in a second.

Yes, you are correct.

SOH CAH TOA can be a good mnemonic aid for remembering trigonometric funtions.

I hope so Heather :)

Thank you Chris.  That is sooo very sweet of you.

I asked CPhill if he would help me moderate this forum over a year ago.  March14 wasn't it Chris? 

(Correction, Chris joined the forum on the March 13th 2014 and became a moderator on May11th 2014)

We have worked as a team ever since.  It has always been a huge pleasure to me to have Chris by my side.  We have become great friends and we are both very proud of how this forum has matured and all the wonderful people that it has attracted.

Thanks also MG

And thank you to all you wonderful people who have supported us and helped make this Web2calc forum such a great place to learn and be happy.

(The forum is lovingly known as the Magical Realm of Camelot)

The flowers a very beautiful.    

Mmmmmm....somehow.....I knew this would be the "follow-up" question......!!!!! ......LOL!!!

As they say....."tune in later"....for the answer(s).....

finally the fighting has stopped. thx melody

:)

.......Just a whole bunch of numbers, letters and symbols!.....

Hey......that kinda' sounds like.......MATH....!!!!

Hahah!

The first time i teach a grown up.

Lol.

Ok, we'll trade in exchange for LaTeX give me 99% of your points!

Just joking...We'll need someone like you as Moderator I'm not sure I'll do great.

LaTeX looks hard but once leart it actually isn't.

Just a whole bunch of numbers, letters and symbols!