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  1. #1
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    Angry math!

    hi hows it going? i hope good but for me not that great cuz I don't get math!!!
    I have been like trying to understand this question and it it taken me like one hour and it probably really easy but I am really fustrated!
    george entered a function into his calculator andfound the following partail sums
    s1=0.0016
    s2= 0.0096
    s3= 0.0496
    s4= 0.2496
    s5= 1.2496

    determine the genral term of the corresponding sequence

    Thanks for all your help!
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  2. #2
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    Quote Originally Posted by cutie4ever View Post
    hi hows it going? i hope good but for me not that great cuz I don't get math!!!
    I have been like trying to understand this question and it it taken me like one hour and it probably really easy but I am really fustrated!
    george entered a function into his calculator andfound the following partail sums
    s1=0.0016
    s2= 0.0096
    s3= 0.0496
    s4= 0.2496
    s5= 1.2496
    S_1=a_1=.0016
    S_2=a_1+a_2=.0096\to a_2=.008
    S_3=a_1+a_2+a_3=.0496\to a_3=.04
    S_4=a_1+a_2+a_3+a_4=.2496\to a_4=.2
    S_5=a_1+a_2+a_3+a_4+a_5=1.2496\to a_5=1
    Thus,
    .0016,.008,.04,.2,1
    It seems that this is a geometric series,
    Because you have,
    16,8,4,2,1....
    Powers of two.
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  3. #3
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    Hello, cutie4ever!

    George entered a function into his calculator and found the following partail sums:

    . . \begin{array}{ccccc}s_1 = 0.0016\\s_2 = 0.0096\\ s_3 = 0.0496 \\ s_4 = 0.2496 \\ s_5 = 1.2496\end{array}

    Determine the general term of the corresponding sequence.

    If you covert the decimals to fractions, a pattern emerges.

    \begin{array}{cccccc}s_1 & = & \frac{16}{10,000} \\ s_2 & = & \frac{16}{10,000} + \frac{8}{1000}\\s_3 & = & \left(\frac{16}{10,000} + \frac{8}{1000}\right) + \frac{4}{100}\\s_4 & = & \left(\frac{16}{10,000} + \frac{8}{1000} + \frac{4}{100}\right) + \frac{2}{10}\\ \vdots & & \vdots\end{array}

    Each sum is the preceding sum plus a power of: \frac{2}{10} = \frac{1}{5} = 5^{-1}

    It begins with: \frac{16}{10,000} = 5^{-4} . and we add: 5^{-3},\;5^{-2},\;5^{-1},\;\hdots

    Hence, the series is: . s \:=\:5^{-4} + 5^{-3} + 5^{-2} + 5^{-1} + \hdots


    Therefore, the general term is: . a_n\;=\;5^{n-5}

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