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? asked in Science & MathematicsMathematics · 2 weeks ago

Find the sum of the infinite series below?

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4 Answers

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  • Engr. Ronald
    Lv 7
    2 weeks ago

    Given 

    a₁ = 36

    r = -2/3

    ............a₁

    S = -----------

    .........1 - r

    ............ 36

    S =  -------------

    ........1 -(-2/3)

    S = 108/5 Answer//

    Answer is B. 108/5

  • Krishnamurthy
    Lv 7
    2 weeks ago

    36 - 24 + 16 - 32/3 + ... 

    Infinite sum:

    sum_(n=1)^∞ (-2)^(1 + n) 3^(3 - n) = 108/5 = 21.6

    Answer choice: 

    B. 108/5

  • ?
    Lv 7
    2 weeks ago

    Each step is -2/3 of the previous one, (so, a geometric series)

    Use infinite sum formula S = a/(1 – r) = 36/(1 + 2/3) = 21.6, (which was B)

  • Pope
    Lv 7
    2 weeks ago

    That is a geometric series with initial term 36 and common ratio -2/3.

    36/[1 - (-2/3)] = 36/(5/3) = 108/5

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