Algebra

For the geometric series given by 2+4+8+... , which of the following statements is FALSE?



Select one:

a. S200>S199

b. S200>a200

c. S1=a1

d. None of the other 3 statements here are False.

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  2. 👎
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  1. In a geometric sequence:

    an = a1 ∙ rⁿ⁻¹

    Sum of the first n terms of a geometric sequence:

    Sn = a1 ∙ ( 1 − rⁿ ) / ( 1− r )

    where

    a1 = first term

    r is the common ratio

    In tis case

    a1 = 2 , r = 2

    so

    Sn = a1 ∙ ( 1 − rⁿ ) / ( 1− r )

    S199 = 2 ∙ ( 1 − 2¹⁹⁹ ) / ( 1− 2 )

    S199 = 2 ∙ ( 1 − 2¹⁹⁹ ) / ( - 1 )

    S199 = - 2 ∙ ( 1 − 2¹⁹⁹ ) = 1.6069380442589902755419620923412 ∙ 10⁶⁰

    S200 = 2 ∙ ( 1 − 2²⁰⁰ ) / ( 1− 2 )

    S200 = 2 ∙ ( 1 − 2²⁰⁰ ) / ( - 1 )

    S200 = - 2 ∙ ( 1 − 2²⁰⁰ ) = 3.2138760885179805510839241846823 ∙ 10⁶⁰

    S200 > S199

    3.2138760885179805510839241846823 ∙ 10⁶⁰ > 1.6069380442589902755419620923412 ∙ 10⁶⁰

    True

    an = a ∙ rⁿ⁻¹

    a200 = 2 ∙ 2¹⁹⁹ = 2²⁰⁰ = 1.6069380442589902755419620923412 ∙ 10⁶⁰

    S200 > a200

    3.2138760885179805510839241846823 ∙ 10⁶⁰ > 1.6069380442589902755419620923412 ∙ 10⁶⁰

    True

    S1 = a1

    2 = 2

    True

    d. None of the other 3 statements here are False.

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