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OfflineCoaster
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Compute the sum
    #8027956 - 02/15/08 04:05 PM (15 years, 11 months ago)

7+13+19+25+...+673
took me about 10 minutes i wonder if any1 else can do it
ill give u a clue, if any1 even cares which no1 does, there is 112 terms


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OfflineCoaster
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Re: Compute the sum [Re: Coaster]
    #8027971 - 02/15/08 04:11 PM (15 years, 11 months ago)



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OfflinePilzeEssen


Registered: 12/24/07
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Re: Compute the sum [Re: Coaster]
    #8027982 - 02/15/08 04:13 PM (15 years, 11 months ago)

+6 all the way up


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"The soul has greater need of the ideal than of the real. It is by the real that we exist, it is by the ideal that we live."

If you want to get a hold of me, my email address is in my profile. Just click on my screen name. I got banned from using private messages cause I didn't follow the rules... :frown:


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InvisibleFerris
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Re: Compute the sum [Re: PilzeEssen]
    #8027990 - 02/15/08 04:15 PM (15 years, 11 months ago)

Isn't that just 112!*6+1

Edit: nevermind, that ! is for multiplication.


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OfflinePilzeEssen


Registered: 12/24/07
Posts: 7,312
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Re: Compute the sum [Re: PilzeEssen]
    #8027998 - 02/15/08 04:17 PM (15 years, 11 months ago)

31,37,43,49,55,61,67,73,79,85,91,97,103,109,115,121,127,133,139,145,151,157,163...etc....

am i wrong?


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"The soul has greater need of the ideal than of the real. It is by the real that we exist, it is by the ideal that we live."

If you want to get a hold of me, my email address is in my profile. Just click on my screen name. I got banned from using private messages cause I didn't follow the rules... :frown:


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InvisibleFerris
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Re: Compute the sum [Re: PilzeEssen]
    #8028012 - 02/15/08 04:20 PM (15 years, 11 months ago)

Ok, I think it is 112 divided by 2, squared, times 6, plus 1.

18,817.

Sounds at least close to me.


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Offlinekarma35
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Registered: 09/07/07
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Re: Compute the sum [Re: Coaster]
    #8028019 - 02/15/08 04:21 PM (15 years, 11 months ago)

Took about a minute. :-) Here's are the steps to solving it fast:

7 + 13 + 19 + ... + 673

First recognize that the sequence can be represented as follows:

= (6*1 + 1) + (6*2 + 1) + (6*3 + 1) + ... + (6*112 + 1)

Now bring out all of the "+1" terms, which equal 112.

= 6*1 + 6*2 + 6*3 + ... + 6*112 + 112

Now factor out the sixes:

= 6 * (1 + 2 + 3 + ... + 112) + 112

Now it looks tedious, but it's not if you know the "trick" to adding a long series of numbers:

= 6 * ((112 +1) + (111 + 2) + (110 + 3) + ... + (57 + 56)) + 112

Notice that all of the parenthesized terms add up to 113, and there are exactly 56 of them. So the long tedious addition reduces to a simple multiplication:

= 6 * (113 * 56) + 112

And now just type them in to a calculator:

= 38080

:-)


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InvisibleWhiskeyClone
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Re: Compute the sum [Re: karma35]
    #8028042 - 02/15/08 04:26 PM (15 years, 11 months ago)

:handth:


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Welcome evermore to gods and men is the self-helping man.  For him all doors are flung wide: him all tongues greet, all honors crown, all eyes follow with desire.  Our love goes out to him and embraces him, because he did not need it.

~ R.W. Emerson, "Self-Reliance"

:heartpump:


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InvisibleFerris
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Re: Compute the sum [Re: WhiskeyClone]
    #8028074 - 02/15/08 04:34 PM (15 years, 11 months ago)

We'll be launching Shroomery satellites in no time.


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OfflineCoaster
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Re: Compute the sum [Re: karma35]
    #8028089 - 02/15/08 04:38 PM (15 years, 11 months ago)

Quote:

karma35 said:
Took about a minute. :-) Here's are the steps to solving it fast:

7 + 13 + 19 + ... + 673

First recognize that the sequence can be represented as follows:

= (6*1 + 1) + (6*2 + 1) + (6*3 + 1) + ... + (6*112 + 1)

Now bring out all of the "+1" terms, which equal 112.

= 6*1 + 6*2 + 6*3 + ... + 6*112 + 112

Now factor out the sixes:

= 6 * (1 + 2 + 3 + ... + 112) + 112

Now it looks tedious, but it's not if you know the "trick" to adding a long series of numbers:

= 6 * ((112 +1) + (111 + 2) + (110 + 3) + ... + (57 + 56)) + 112

Notice that all of the parenthesized terms add up to 113, and there are exactly 56 of them. So the long tedious addition reduces to a simple multiplication:

= 6 * (113 * 56) + 112

And now just type them in to a calculator:

= 38080

:-)



fuck ya dood ur awsome
+5 shrooms 4 u
im glad u took the time to do it, u are 1 exellent shroomite


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Offlineskydog
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Re: Compute the sum [Re: karma35]
    #8028094 - 02/15/08 04:39 PM (15 years, 11 months ago)

Ladies and Gentlemen, Carl Friedrich Gauss! :rainbowcloud:


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OfflineCoaster
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Re: Compute the sum [Re: skydog]
    #8028104 - 02/15/08 04:43 PM (15 years, 11 months ago)

hell ya gauss is my homie
he pops up all over the place, his influence is so great its hard to comprehend


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Offlinekarma35
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Registered: 09/07/07
Posts: 33
Last seen: 5 months, 9 days
Re: Compute the sum [Re: Coaster]
    #8028201 - 02/15/08 05:09 PM (15 years, 11 months ago)

Doh, just realized there's a faster method that takes about 15 seconds:

7 + 13 + 19 + ... + 673

If you realize this is just (6*1 + 1) + (6*2 + 1) + ... + (6*112 + 1), then it's clear that there are 112 terms, and that each term is 6 more than the previous one. So, you can use the "fast-addition" trick as before, but skip the intermediate steps:

= (673 + 7) = (667 + 13) + ...

This time each parenthesized term adds up to 680, and just as before, there'll be 56 parenthesized terms (remember, you're just pairing up the original 112 numbers).

= 680 * 56

= 38080

Now go impress your friends and family :-)


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OfflineCoaster
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Registered: 05/22/06
Posts: 33,501
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Re: Compute the sum [Re: karma35]
    #8028256 - 02/15/08 05:18 PM (15 years, 11 months ago)

dam dood u amaze me
fawking awsomeness


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