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19 March, 00:10

Given a geometric series, multiply every term by the same nonzero constant c. The resulting series must also be geometric. True False b) A new series is obtained from a geometric series by taking the reciprocal of each term. The new series must also be geometric. True False

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  1. 19 March, 03:11
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    True True

    Step-by-step explanation:

    1. In the original series, the terms are ...

    a1 + a1·r + a1·r² + ...

    Multiplying each term by c, we get ...

    (a1·c) + (a1·c) ·r + (a1·c) ·r² + ...

    This new series is a geometric series with common ratio r and first term a1·c.

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    2. In the original series, the terms are ...

    a1 + a1·r + a1·r² + ...

    Taking the reciprocal of each term, the new series is ...

    (1/a1) + (1 / (a1·r)) + (1 / (a1·r²)) + ...

    = (1/a1) + (1/a1) (1/r) + (1/a1) (1/r) ² + ...

    The new series is a geometric series with common ratio 1/r and first term 1/a1.
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