12 окт. 2016 г. · You can distribute now and write (x−1)∞∑n=1xn2n+1=∞∑n=1xn+12n+1−∞∑n=1xn2n+1. Now re-index the first sum and combine like powers of x to find the ...

2 нояб. 2020 г. · Simple: they rewrote the fraction as: x−1x+2=(x+2)−3x+2=1−3x+2=1−3211+x2. and used the expansion of 11+u.

23 янв. 2019 г. · The function doesn't have a unique series representation; you found the one centered at −1 and the formula is correct.

29 мар. 2013 г. · I first find a representation for 1/1−x ( which is the integral of 1/(1−x)2 ) and then derive to get back to the representation for 1/(1−x)2.

29 окт. 2016 г. · The polynomial x2+x+1=Φ3(x) has no real roots, but it vanishes at x=e±2πi3. In particular, by setting ω=exp(2 ...

18 мар. 2016 г. · I have to find a power series representation for f(x)=x−1x+2. In rearranging the function so as to attain a form suitable for representation ...

8 мая 2018 г. · There is another way of doing this computation. You correctly pointed out that: 11−x=∞∑n=0xn.

29 янв. 2020 г. · Any way you get a power series that converges to your function will give the same series. What way you select depends on taste/ease/familiarity.

31 окт. 2016 г. · We can use this: 11−x∞∑n=0anxn=∞∑n=0(a0+a1+⋯+an)xn. Expand 11−x2,. 11−x2=∞∑n=0x2n=∞∑k=01+(−1)k2xk. Therefore, 11−x∞∑ ...

6 авг. 2020 г. · (a) Find a power series representation for the function f(x)=1x with the center of the series at a=1 by realizing that f is the sum of a ...