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Math Help - Geometric Series - Find it's sum

  1. #1
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    Geometric Series - Find it's sum

    Can you verify if my answer is correct for this problem?

    Answer: sqrt(5)/sqrt(5)-1
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  2. #2
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    Re: Geometric Series - Find it's sum

    Hello, l flipboi l

    Can you verify if my answer is correct for this problem?

    . . \sum^{\infty}_{n=0} \frac{1}{(\sqrt{5})^n}

    \text{Answer: }\:\frac{\sqrt{5}}{\sqrt{5}-1} . Yes!

    \text{Infinite geometric series with first term }a = 1\,\text{ and common ratio }r = \tfrac{1}{\sqrt{5}}

    . . \text{Sum} \:=\:\frac{a}{1-r} \;=\;\frac{1}{1-\frac{1}{\sqrt{5}}} \;=\;\frac{\sqrt{5}}{\sqrt{5}-1}
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  3. #3
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    Re: Geometric Series - Find it's sum

    Quote Originally Posted by l flipboi l View Post
    Can you verify if my answer is correct for this problem?

    Answer: sqrt(5)/sqrt(5)-1
    S=\frac{1}{\sqrt{5}^0}+\frac{1}{\sqrt{5}^1}+......  .

    S-1=\frac{1}{\sqrt{5}^1}+\frac{1}{\sqrt{5}^2}+.....

    \sqrt{5}(S-1)=1+\frac{1}{\sqrt{5}^1}+....

    \sqrt{5}S-\sqrt{5}=S

    S\left(\sqrt{5}-1\right)=\sqrt{5}

    S=\frac{\sqrt{5}}{\sqrt{5}-1}
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    Re: Geometric Series - Find it's sum

    Thank you, both!
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