Looks like the series is
![\displaystyle\sum_{n=1}^\infty n^{-13}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Csum_%7Bn%3D1%7D%5E%5Cinfty%20n%5E%7B-13%7D)
We have
![\displaystyle\sum_{n=1}^\infty\frac1{n^{13}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Csum_%7Bn%3D1%7D%5E%5Cinfty%5Cfrac1%7Bn%5E%7B13%7D%7D%3C%5Cint_1%5E%5Cinfty%5Cfrac%7B%5Cmathrm%20dx%7D%7Bx%5E%7B13%7D%7D)
![\displaystyle=-\frac1{12x^{12}}\bigg|_{x=1}^{x\to\infty}](https://tex.z-dn.net/?f=%5Cdisplaystyle%3D-%5Cfrac1%7B12x%5E%7B12%7D%7D%5Cbigg%7C_%7Bx%3D1%7D%5E%7Bx%5Cto%5Cinfty%7D)
![\displaystyle=-\frac1{12}\left(\lim_{x\to\infty}\frac1{x^{12}}-1\right)=\frac1{12}](https://tex.z-dn.net/?f=%5Cdisplaystyle%3D-%5Cfrac1%7B12%7D%5Cleft%28%5Clim_%7Bx%5Cto%5Cinfty%7D%5Cfrac1%7Bx%5E%7B12%7D%7D-1%5Cright%29%3D%5Cfrac1%7B12%7D)
Therefore the sum converges, since its value is smaller than
![\dfrac1{12}](https://tex.z-dn.net/?f=%5Cdfrac1%7B12%7D)
.
Answer:
C. 3 & -6
Step-by-step explanation:
x² + 3x -18 = 0
x² + 6x - 3x - 18 = 0
(x + 6)(x - 3) = 0
Ratio = 2:3 = 2/5
Distance between the x coordinates: 3
Distance between the y coordinates: 7
x: 3 * 2/5 = 1.2
y: 7 * 2/5 = 2.8
x coordinate of point: 6 - 1.2 = 4.8
y coordinate of point: 1 + 2.8 = 3.8
So the point that divides the segment AB in the ratio of 2:3 is (4.8 , 3.8) or (24/5 , 19/5)
Hope this helps :)
My guess is the answer is b but you may want to get another answer from someone else
Answer:
1
Step-by-step explanation: