Answer: x-5+5+5
Step-by-step explanation:
Answer:
8.91
Step-by-step explanation:
Given: 0.95 = log x,
we can conclude that:
0.95 log x
10 = 10
0.95
which in turn is equivalent to x = 10 whose value is 8.91
Answer:
find 9% of 12
12 times 9 divided by 100
108/100
$1.08
12+1.08
Your mean costs $13.08
-Have a nice meal!
Assuming the series is
![\displaystyle\sum_{n\ge1}\frac{x^n}{2n-1}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Csum_%7Bn%5Cge1%7D%5Cfrac%7Bx%5En%7D%7B2n-1%7D)
The series will converge if
![\displaystyle\lim_{n\to\infty}\left|\frac{\frac{x^{n+1}}{2(n+1)-1}}{\frac{x^n}{2n-1}}\right|](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Clim_%7Bn%5Cto%5Cinfty%7D%5Cleft%7C%5Cfrac%7B%5Cfrac%7Bx%5E%7Bn%2B1%7D%7D%7B2%28n%2B1%29-1%7D%7D%7B%5Cfrac%7Bx%5En%7D%7B2n-1%7D%7D%5Cright%7C%3C1)
We have
![\displaystyle\lim_{n\to\infty}\left|\frac{\frac{x^{n+1}}{2(n+1)-1}}{\frac{x^n}{2n-1}}\right|=|x|\lim_{n\to\infty}\frac{\frac1{2n+1}}{\frac1{2n-1}}=|x|-\lim_{n\to\infty}\frac{2n-1}{2n+1}=|x|](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Clim_%7Bn%5Cto%5Cinfty%7D%5Cleft%7C%5Cfrac%7B%5Cfrac%7Bx%5E%7Bn%2B1%7D%7D%7B2%28n%2B1%29-1%7D%7D%7B%5Cfrac%7Bx%5En%7D%7B2n-1%7D%7D%5Cright%7C%3D%7Cx%7C%5Clim_%7Bn%5Cto%5Cinfty%7D%5Cfrac%7B%5Cfrac1%7B2n%2B1%7D%7D%7B%5Cfrac1%7B2n-1%7D%7D%3D%7Cx%7C-%5Clim_%7Bn%5Cto%5Cinfty%7D%5Cfrac%7B2n-1%7D%7B2n%2B1%7D%3D%7Cx%7C%3C1)
So the series will certainly converge if
![-1](https://tex.z-dn.net/?f=-1%3Cx%3C1)
, but we also need to check the endpoints of the interval.
If
![x=1](https://tex.z-dn.net/?f=x%3D1)
, then the series is a scaled harmonic series, which we know diverges.
On the other hand, if
![x=-1](https://tex.z-dn.net/?f=x%3D-1)
, by the alternating series test we can show that the series converges, since
![\left|\dfrac{(-1)^n}{2n-1}\right|=\dfrac1{2n-1}\to0](https://tex.z-dn.net/?f=%5Cleft%7C%5Cdfrac%7B%28-1%29%5En%7D%7B2n-1%7D%5Cright%7C%3D%5Cdfrac1%7B2n-1%7D%5Cto0)
and is strictly decreasing.
So, the interval of convergence for the series is
![-1\le x](https://tex.z-dn.net/?f=-1%5Cle%20x%3C1)
.
Answer:24 and 10
Step-by-step explanation:24-10=34 24-10=14