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Math Help - Sum of a geometric series--am I doing this right?

  1. #1
    Member MathBlaster47's Avatar
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    Sum of a geometric series--am I doing this right?

    The problem asks me to find the sum of the first twenty numbers in the sequence:1+8+64+512+.....

    So I applied the formula:  S_{20}=\frac{1(1-8^20)}{1-8}

    I came out with the number:164,703,072,086,692,425.
    I used a calculator, of course.

    Am I doing it right?
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  2. #2
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    Quote Originally Posted by MathBlaster47 View Post
    The problem asks me to find the sum of the first twenty numbers in the sequence:1+8+64+512+.....

    So I applied the formula:  S_{20}=\frac{1(1-8^20)}{1-8}

    I came out with the number:164,703,072,086,692,425.
    I used a calculator, of course.

    Am I doing it right?
    Yes Mathblaster47,

    it's a geometric series, a=1, r=8.

    S_n=\frac{a(1-r^n)}{1-r}=\frac{a(r^n-1)}{r-1}
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  3. #3
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    Quote Originally Posted by MathBlaster47 View Post
    The problem asks me to find the sum of the first twenty numbers in the sequence:1+8+64+512+.....

    So I applied the formula:  S_{20}=\frac{1(1-8^20)}{1-8}

    I came out with the number:164,703,072,086,692,425.
    I used a calculator, of course.

    Am I doing it right?
    Looks good to me


    S_{20}=\frac{1(1-8^{20})}{1-8}
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  4. #4
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    That is the correct formula, so if you entered it into your calculator correctly, the answer is correct.
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  5. #5
    Super Member Quacky's Avatar
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    So you know that r = common ratio, which is in this case 8. It's the Rate of increase and decrease, is how I like to think about it.
    N=20.
    Your first value is 1
    The formula for a geometric series is:

    \sum n = \frac{a(1-r^n)}{1-r}

    So, substituting the values in gives:

    \sum 20 = \frac{1(1-8^{20})}{1-8}

    I get the same result.

    Edit: Dang! was beaten by several people. Meh, at least you can be fairly certain.
    Last edited by Quacky; February 16th 2010 at 02:44 PM. Reason: I really need to start looking for typos
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  6. #6
    Member MathBlaster47's Avatar
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    Ok then....is there a term for the size of the number? I know it goes past trillion, but heck.....that is a big number!

    Thank you for the quick replies guys!
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  7. #7
    Super Member Quacky's Avatar
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    It would depend upon your country.

    Million, Billion, Trillion... explains that your number is...

    'one hundred and sixty-four quadrillion, 7 hundred and three trillion,72 billion,86 million, six hundred and ninety-two thousand,four hundred and twenty-five.'
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  8. #8
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    Quote Originally Posted by MathBlaster47 View Post
    Ok then....is there a term for the size of the number? I know it goes past trillion, but heck.....that is a big number!

    Thank you for the quick replies guys!
    Yeah!

    it's 164.703072087 quadrillion.
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  9. #9
    Member mathemagister's Avatar
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    Quote Originally Posted by MathBlaster47 View Post
    Ok then....is there a term for the size of the number? I know it goes past trillion, but heck.....that is a big number!

    Thank you for the quick replies guys!
    I would call it 164 quadrillion,703 trillion,72 billion, 86 million, 692 thousand and 425, but that's just my way of saying it. Some people would call it 164,703 billion, 72,086 million, 692,425. That's how the world works
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  10. #10
    Member MathBlaster47's Avatar
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    Quote Originally Posted by Quacky View Post
    It would depend upon your country.

    Million, Billion, Trillion... explains that your number is...

    'one hundred and sixty-four quadrillion, 7 hundred and three trillion,72 billion,86 million, six hundred and ninety-two thousand,four hundred and twenty-five.'
    Quote Originally Posted by Archie Meade View Post
    Yeah!

    it's 164.703072087 quadrillion.
    Wow.....Who wouldn't want a bank account that big....
    Again thank you for your help!
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  11. #11
    Member mathemagister's Avatar
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    Quote Originally Posted by mathemagister View Post
    I would call it 164 quadrillion,703 trillion,72 billion, 86 million, 692 thousand and 425, but that's just my way of saying it. Some people would call it 164,703 billion, 72,086 million, 692,425. That's how the world works
    By the way, when I wrote it in the second format, I know for a fact that some languages actually do it the second way (German for example).
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  12. #12
    Junior Member StonerPenguin's Avatar
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    Haha! Yeah, MathBlaster47, you're doing the American School of Correspondence's Algebra 2 course, me too! And it looks like we're about even in our progress so it's nice to check my answers since you have the same questions. The question alse reaaaallly bugged me, especially since none of the example problems are nearly this 'HUEG'. Moreover, they didn't even give you enough room to write this gia-huge-ic number, makes me worry that it's wrong but seeing all these people agreeing makes me feel better.

    BTW, where did you find a calculator the would go that high!? I had to find 8^2 .^0 and divide it by 7 on paper! And then I added all the sums together manually to confirm my answer (which took quite a while...). Where is this great and mighty calculator!?
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  13. #13
    Member MathBlaster47's Avatar
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    Quote Originally Posted by StonerPenguin View Post
    Haha! Yeah, MathBlaster47, you're doing the American School of Correspondence's Algebra 2 course, me too! And it looks like we're about even in our progress so it's nice to check my answers since you have the same questions. The question alse reaaaallly bugged me, especially since none of the example problems are nearly this 'HUEG'. Moreover, they didn't even give you enough room to write this gia-huge-ic number, makes me worry that it's wrong but seeing all these people agreeing makes me feel better.

    BTW, where did you find a calculator the would go that high!? I had to find 8^2 .^0 and divide it by 7 on paper! And then I added all the sums together manually to confirm my answer (which took quite a while...). Where is this great and mighty calculator!?
    Well......I used Microsoft math to do the calculations, and presto!
    There was the improbably large answer!
    Tis nice to see another ASC student around, I hope you do well in the exams!
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  14. #14
    Junior Member StonerPenguin's Avatar
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    Quote Originally Posted by MathBlaster47 View Post
    Well......I used Microsoft math to do the calculations, and presto!
    There was the improbably large answer!
    Tis nice to see another ASC student around, I hope you do well in the exams!
    Ah thank you, thank you! I think my mom found out that we had that program the other day, I'll be sure to use it then. Thanks for the luck, I hope you do well too! I don't know about you but I am so ready to be done with this, I'm on Chapter 15 now, the final 100 pages~ then I just have finish Chemistry...

    I have a few questions I wanna ask you, I guess I'll p.m. ya.
    ------------
    EDIT; Okay, so like, I figured out that you have to have 15 posts before you can send P.M.s, but I learned this *after* I had completely typed up my message, hit send and lost everything I typed. Ya'll don't have a system that tells you *before* you send messages? Or the whole PM system should be disabled to newbies then D:<
    Last edited by StonerPenguin; February 22nd 2010 at 07:05 AM.
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