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February 27th, 2012, 04:01 PM   #1
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Find the sum of the first 50 terms

Find the sum of the first 50 terms of the following sequence:
1 + 3 - 5 + 7 + 9 - 11 + 13 + 15 - 17 + ...
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February 27th, 2012, 05:36 PM   #2
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Re: Find the sum of the first 50 terms

We have the sum S given by:







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February 27th, 2012, 05:45 PM   #3
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Re: Find the sum of the first 50 terms

We could also write:

S = 1 + 3 - 5 + 7 + 9 - 11 + ... - 89 + 91 + 93 - 95 + 97 + 99

S = 99 + 97 - 95 + 93 + 91 - 89 + ... - 11 + 9 + 7 - 5 + 3 + 1

Adding we get:

2S = 16(100 + 100 - 100) + 100 + 100 = 1800

S = 900
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February 27th, 2012, 05:56 PM   #4
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Re: Find the sum of the first 50 terms

Mark looks like Carl Friedrich Gauss to me .
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February 27th, 2012, 06:09 PM   #5
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Re: Find the sum of the first 50 terms



[attachment=0:21x2xpqg]gaussplate.jpg[/attachment:21x2xpqg]
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February 27th, 2012, 07:53 PM   #6
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Re: Find the sum of the first 50 terms

Quote:
Originally Posted by MarkFL
We could also write:
S = 1 + 3 - 5 + 7 + 9 - 11 + ... - 89 + 91 + 93 - 95 + 97 + 99
S = 99 + 97 - 95 + 93 + 91 - 89 + ... - 11 + 9 + 7 - 5 + 3 + 1
Similarly; looking at it as 2 series:

1 + 3 + 5 + 7 + ....... + 95 + 97 + 99 = 2500

2(-5 - 11 - 17 ....... - 89 - 95) = -1600

Throwing that mess in the arithmetic series formula:
50(1 + 99) / 2 - 2[16(5 + 95) / 2] = 900
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February 28th, 2012, 03:38 AM   #7
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Re: Find the sum of the first 50 terms

Hello, stevecowall!

And yet another approach . . .


Quote:
Find the sum of the first 50 terms of the following sequence:
[color=beige]. . [/color]1 + 3 - 5 + 7 + 9 - 11 + 13 + 15 - 17 + ...











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February 28th, 2012, 08:40 AM   #8
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The mean of the first 2 terms is 2.
The mean of the first 5 terms is 3.
The mean of the first 8 terms is 4.
...
The mean of the first 50 terms is 18, so their sum is 900.
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February 28th, 2012, 12:59 PM   #9
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Re:

Quote:
Originally Posted by skipjack
The mean of the first 2 terms is 2.
The mean of the first 5 terms is 3.
The mean of the first 8 terms is 4.
...
The mean of the first 50 terms is 18, so their sum is 900.
OH WOW! This is nice! Do you have 'skipjack' on your license plate?
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