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mathmath333

  • one year ago

Iterative Series Question.

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  1. mathmath333
    • one year ago
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    \(\large \color{black}{\begin{align} &\normalsize \text{The nth element of the series is represented as:} \hspace{.33em}\\~\\ &X_{n}=(-2)^{n}X_{n-1} \hspace{.33em}\\~\\ &\normalsize \text{if} \ X_{0}=x\ \normalsize \text{and }\ x>0\ \hspace{.33em}\\~\\ &\normalsize \text{then the following is always true} \hspace{.33em}\\~\\ &(a.)\ X_{n} \ \normalsize \text{is positive if n is even} \hspace{.33em}\\~\\ &(b.)\ X_{n} \ \normalsize \text{is positive if n is odd} \hspace{.33em}\\~\\ &(c.)\ X_{n} \ \normalsize \text{is negative if n is even} \hspace{.33em}\\~\\ &(d.) \normalsize \text{None of these} \hspace{.33em}\\~\\ \end{align}}\)

  2. perl
    • one year ago
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    Pick \(\large X_o=1 \) , that seems easiest.

  3. mathmath333
    • one year ago
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    i think both option a and b are correct, what u think

  4. mathmath333
    • one year ago
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    ohk thnks it looks option d is the correct one.

  5. perl
    • one year ago
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    The the first three values are \[\Large{ X_o = 1 \\ \\X_1 = (-2)^1\cdot X_0= -2 \cdot 1 = -2 \\X_2 = (-2)^2\cdot X_1 = (-2)^2 \cdot (-2)= -8 \\X_3 = (-2)^3\cdot X_2 = (-8)(-8)=64 \\ X_4 = (-2)^4 \cdot X_3 = 16 \cdot 64 = 1024 } \]

  6. perl
    • one year ago
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    I agree

  7. zzr0ck3r
    • one year ago
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    Do you mean series or sequence?

  8. zzr0ck3r
    • one year ago
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    do you mean partial sum or term?

  9. zzr0ck3r
    • one year ago
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    nth element of a series does not make sense...

  10. perl
    • one year ago
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    @zzr0ck3r How about the nth term of the series?

  11. perl
    • one year ago
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    for example 1 + 2 + 3 + 4 + ... 1 is the first term 2 is the second term 3 is the third term. etc It would just be easier to say the nth term of the sequence whose terms are come from a series.

  12. zzr0ck3r
    • one year ago
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    yes for sure "term" makes sense, but as the question was phrased I was not sure if they were asking about the nth element in the sequence of partial sums of the series or just the nth element in the sequence.

  13. perl
    • one year ago
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    I don't think she meant partial sum

  14. zzr0ck3r
    • one year ago
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    right I think I should have read first :)

  15. perl
    • one year ago
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    agreed, it was ambiguous :)

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