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Math Help - How To Find The Constant And N Of Expanding (Pascal's Triangle)

  1. #1
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    How To Find The Constant And N Of Expanding (Pascal's Triangle)

    I know the answer to these questions, but want to know how.

    #1 The 10th term of the expansion of (x-(1/2))^n is -(1001/256)x^5

    Find N.

    The answer is 14. How do we get this? (I got it through trial and error, but I'm sure there is an easier way...)

    #2 Which term in the expansion of ((1/(2x^2)) - x^3)^10 is a constant?

    The answer is the 5th term.

    I used trial and error for this one too. Though I"m sure there is an easier way too.
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  2. #2
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    Quote Originally Posted by AlphaRock View Post
    I know the answer to these questions, but want to know how.

    #1 The 10th term of the expansion of (x-(1/2))^n is -(1001/256)x^5

    Find N.

    The answer is 14. How do we get this? (I got it through trial and error, but I'm sure there is an easier way...)

    #2 Which term in the expansion of ((1/(2x^2)) - x^3)^10 is a constant?

    The answer is the 5th term.

    I used trial and error for this one too. Though I"m sure there is an easier way too.

    Use the binomial theorem

    (a+n)^n=\sum_{k=0}^{n}\binom{n}{k}a^{n-k}b^{k}

    Since we have the x^5 term we know that

    n-k=5

    Also since we are on the 10th term we know k=9 (remember the index starts at 0 not 1) so we get

    n-9=5 \iff n=14

    See if you can figure out the next one with this theorem.

    Good luck
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  3. #3
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    Quote Originally Posted by TheEmptySet View Post
    Use the binomial theorem

    (a+n)^n=\sum_{k=0}^{n}\binom{n}{k}a^{n-k}b^{k}

    Since we have the x^5 term we know that

    n-k=5

    Also since we are on the 10th term we know k=9 (remember the index starts at 0 not 1) so we get

    n-9=5 \iff n=14

    See if you can figure out the next one with this theorem.

    Good luck
    Thanks for replying to my thread, TheEmptySet!

    I'm having trouble understanding the sigma notation for this. It's been a while since we did this and I lent my math binder to my friend to help him, thinking I would not need it for this.

    Can someone help me understand how to do the binomial theorem for this? I'm a quick learner.
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