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January 14th, 2013, 04:00 AM   #1
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sum of the first 50 terms

Determine the sum of the first 50 terms in the series

1+(1/2)+(1/2)^2 +(1/2)^3 +.....

I actually already answered this question but would like to get confirmation on it!

I used formula:

Sn=(a1+an)/2 n

After futher calculations:
an=a1+(n-1) r , r=1/2, a50=?

a50= 51/2

And then using main formula
S50= 1325/2=662.5

Am i correct?
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January 14th, 2013, 05:06 AM   #2
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Re: sum of the first 50 terms

The sum should be bounded above by 2, right?
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January 14th, 2013, 05:17 AM   #3
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Re: sum of the first 50 terms

Yes, but i thought i already did that.

S50= ((1+25.5)/ 2)* 50= 53/2 *25= 1325/2= 662.5
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January 14th, 2013, 05:59 AM   #4
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Re: sum of the first 50 terms

Hello, Agata78!

Quote:









[color=beige]n . . . . .[/color]

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January 14th, 2013, 06:12 AM   #5
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Re: sum of the first 50 terms

Quote:
Originally Posted by Agata78
Yes, but i thought i already did that.

S50= ((1+25.5)/ 2)* 50= 53/2 *25= 1325/2= 662.5
662.5 > 2, so this clearly can't be the answer. soroban has the right idea, above.
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January 14th, 2013, 06:15 AM   #6
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Re: sum of the first 50 terms

I have completely different formula. But i think yours makes more sense then mine!
Thank you
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