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Odinaka_O
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Tyro
Asked: 2020-12-26T09:55:47+00:00 In:

The sum to infinity of a G.P. is \frac{2}{3}, and a=\frac{1}{12}. Find r.

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The sum to infinity of a G.P. is \frac{2}{3}, and a=\frac{1}{12}. Find r.

g.p.sum to infinity

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  2. Sengemegz
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    Moderator

    Sum to infinity(S)=\dfrac{a}{1-r}
    where a=\frac{1}{12}, r=?, S=\frac{2}{3}
    \Rightarrow \frac{2}{3}=\dfrac{\frac{1}{12}}{1-r}
    Cross multiply
    \Rightarrow 2(12(1-r))=3\times 1
    \Rightarrow 24-24r=3
    Collect like term
    \Rightarrow 24-3=24r
    \Rightarrow 21=24r
    Divide both sides by 24
    \therefore r=\frac{21}{24}=\frac{7}{8}

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