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Math Help - cannot figure out this crazy series problem

  1. #1
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    cannot figure out this crazy series problem



    okay so i got the first part of 3 right.. i just dont understand the other 2 parts to this problem.

    for the second part i set n=5 and got that answer but its wrong and i dont understand where i went wrong.. shouldnt it be a6/(1/2)??
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  2. #2
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    \displaystyle \frac{a_6}{1 - \lim_{n \to \infty} \frac{a_{n+1}}{a_n}} \ne 1.38229

    recalculate
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  3. #3
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    \frac{a_{n+1}}{a_n}=\frac{n2^n}{(n+1)2^{n+1}}=\fra  c{1/2}{1+1/n}
    so indeed R_5\le2a_6, which is evidently much less than 1.38229
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  4. #4
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    ive been trying this problem the whole day and still cannot seem to figure it out
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  5. #5
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    \displaystyle \frac{a_6}{1 - \lim_{n \to \infty} \frac{a_{n+1}}{a_n}} = \frac{\frac{1}{6 \cdot 2^6}}{\frac{1}{2}} = \frac{1}{6 \cdot 2^5} = \frac{1}{192} \approx 0.005208
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  6. #6
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    im confused as to how to finished the last problem.. do i use the equation in part B to solve for part C?
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  7. #7
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    ok now i just cant even finish the last part of the problem. what the hell is wrong?
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  8. #8
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    Quote Originally Posted by elpermic View Post
    im confused as to how to finished the last problem.. do i use the equation in part B to solve for part C?
    yes, you use the inequality in part (b) to solve for part (c)


    Quote Originally Posted by elpermic View Post
    ok now i just cant even finish the last part of the problem. what the hell is wrong?
    don't know ... you have shown nothing more than an incorrect answer for part (b) ... how can anyone tell what is "wrong" with either?
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