Enjoy Maths: The first term of an infinite GP is 1 and any term is equal to the sum of all the succeeding terms. Find the series.?

4 Answers

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  • 4 weeks ago
    Favorite Answer

    Here is the solution.

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  • Indica
    Lv 7
    4 weeks ago

    This means that sum of GP = 1+1 = 2 (first term + following terms)

    ∴ 2=1/(1-r) ⟹ r=½ 

  • nbsale
    Lv 6
    4 weeks ago

    1 + 1/2 + 1/4 + 1/8 + ...  is pretty obvious.Let's prove it's the only series.

    Let r be the common ratio, and let S be the sum.

    The series after the first term just looks like r times the series, so using what's given you have:

    1 = rS and therefore

    S = 1/r

    You always have S = first term times 1/(1-r) so you also have

    S = 1/(1-r)

    Therefore 1/(1-r) = 1/r

    Multiply by r(1-r) and you get

    r = 1-r

    2r = 1

    r = 1/2.

    So 1 + 1/2 + 1/4 + ... is the only solution.

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