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Thread: Inequality involving a summation.

  1. #1
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    Inequality involving a summation.

    I have that $\displaystyle 1+\sum_{i=1}^{2n} \dbinom{2n}{i} (-y)^i \geq d$, where $\displaystyle 0 \leq y <1$

    Im trying to figure out why the following inequality holds:

    For any $\displaystyle P \in \{2, 4, 6, 8, ..., 2n\}$

    $\displaystyle 1+\sum_{i=1}^{P} \dbinom{2n}{i} (-y)^i \geq d$

    Why is this??

    I checked it emphirically for $\displaystyle n \leq 30$ and it always holds
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  2. #2
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    Re: Inequality involving a summation.

    Quote Originally Posted by robustor View Post
    I have that $\displaystyle 1+\sum_{i=1}^{2n} \dbinom{2n}{i} (-y)^i \geq d$, where $\displaystyle 0 \leq y <1$

    Im trying to figure out why the following inequality holds:

    For any $\displaystyle P \in \{2, 4, 6, 8, ..., 2n\}$

    $\displaystyle 1+\sum_{i=1}^{P} \dbinom{2n}{i} (-y)^i \geq d$

    Why is this??

    I checked it emphirically for $\displaystyle n \leq 30$ and it always holds
    I expect you'd need to use mathematical induction...
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