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anonymous

  • 5 years ago

what is the middle term of the following exansion and is there a fast way to do it other than just expanding the entire thing? (x - 1/x)^6

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  1. anonymous
    • 5 years ago
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    hi i did some help

  2. anonymous
    • 5 years ago
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    You can use Pascal's triangle to solve this quickly. It goes: \[ \begin{align*} &1\\ 1\quad & \qquad 1\\ 1\qquad &2\qquad 1\\ 1 \qquad 3 &\quad 3 \qquad 1\\ &.... \end{align*} \] This lets you solve the problem more quickly. If you have an expansion \((a+b)^n\), you can look at the \((n+1)\) row of the triangle and use the numbers in it to find the coefficients of the expansion: \[ \begin{align*} &(a+b)^2\\ &\Rightarrow a^2 + 2ab + b \end{align*} \] Note that \(n=2\) and the third rows numbers were [1 2 1], which appeared as coefficients here. The seventh row is [1 6 15 20 15 6 1]. Can you solve your problem from that?

  3. anonymous
    • 5 years ago
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    OR http://www.wolframalpha.com/input/?i=(x+-+1%2Fx)^6

  4. anonymous
    • 5 years ago
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    hi can i attach file

  5. anonymous
    • 5 years ago
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    Include the ^6 in the last link

  6. anonymous
    • 5 years ago
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    interesting, i'll definitely have to look at pascal's triangle more closely, much easier than expanding.

  7. anonymous
    • 5 years ago
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    Yep, it's pretty awesome.

  8. anonymous
    • 5 years ago
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    thank you very much!

  9. anonymous
    • 5 years ago
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    yay

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