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Math Help - Series True/False prob

  1. #1
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    Series True/False prob

    How would I go about proving these statements true or false?

    "If a series is truncated after the nth term, then the error is less than the first omitted them"

    "If r<1, then the series E r^n converges"
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  2. #2
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    Quote Originally Posted by Nerd View Post
    How would I go about proving these statements true or false?

    "If a series is truncated after the nth term, then the error is less than the first omitted them"
    No. (I might not be understanding you correctly.
    "If r<1, then the series E r^n converges"
    What about r=-1?
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  3. #3
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    Quote Originally Posted by ThePerfectHacker View Post
    No. (I might not be understanding you correctly.
    I'm not quite sure what you're trying to say either, but that's what my homework is asking me. True/False. It sounds familiar, but not enough for me to be confident about an answer and guessing is useless, won't help me learn, and won't get me credit (ALL work must be shown)

    Quote Originally Posted by ThePerfectHacker View Post
    What about r=-1?
    Oh...right. -1. Not that hard a number to thunk up...And I've seen that example over a dozen times. Sometimes, it's the obvious that elludes me the most.
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  4. #4
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    [quote=Nerd;47830]How would I go about proving these statements true or false?

    "If a series is truncated after the nth term, then the error is less than the first omitted them"
    quote]


    False. Consider the series:

    S=1 + 2 + 3 + 5 + 0 + .. + 0 + .. = 11

    S(1) = 1

    (where S(n) is the sum of the series truncated to the first n terms)

    The first omited term is 2, but the error is 10.

    RonL
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  5. #5
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    Quote Originally Posted by Nerd View Post
    "If r<1, then the series E r^n converges"
    False, as ImPerfectHacker tries to point out r negative but |r|>=1 gives
    a series which does not converge, but with r<1.

    RonL
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