頁:
[1]
Binomial expansion question and its application
Expand (1-3x)^(-1/2) up to the term x^3.Hence find (12)^(1/2) to the 3 decimal places.
<div></div> 本帖最後由 chongwaikei 於 2013-1-13 05:44 PM 編輯
http://latex.codecogs.com/gif.latex?\begin{align*}%20(1-3x)^{-\frac{1}{2}}&=\sum_{n\geq0}\binom{-\frac{1}{2}}{n}(-3x)^n\\&=1+\frac{3x}{2}+\frac{27x^2}{8}+\frac{135x^3}{16}+O(x^4)\end{align*}
you can finish the 2nd part now
I just can't solve the 2nd part. Would you please tell me how to solve? 本帖最後由 chongwaikei 於 2013-1-14 04:31 PM 編輯
190303458 發表於 2013-1-14 03:06 PM static/image/common/back.gif
I just can't solve the 2nd part. Would you please tell me how to solve?
http://latex.codecogs.com/gif.latex?\\$That%20is%20quite%20easy%20,%20$\frac{1}{\sqrt{1-3x}}=\sqrt{12}\\\\%20$find%20$x$%20and%20sub%20into%20the%20part%20a)%20$\\\\
...<div class='locked'><em>瀏覽完整內容，請先 <a href='member.php?mod=register'>註冊</a> 或 <a href='javascript:;' onclick="lsSubmit()">登入會員</a></em></div> 本帖最後由 chongwaikei 於 2013-1-14 04:54 PM 編輯
I tested the series of the answer in part a).
The series doesn't converge fastly.
If you want to get the answer √12 = 3.464....
maybe you need at least 15 terms of the series
or your teacher only wants the answer of the first 3 terms
<br><br><br><br><br><div></div>
頁:
[1]