The y-intercept is 0 because you can add it to the equation and it won't change your slope.
Q.34
![\sum\limits_{k=1}^{\infty}420\left(1.002\right)^{k-1}](https://tex.z-dn.net/?f=%5Csum%5Climits_%7Bk%3D1%7D%5E%7B%5Cinfty%7D420%5Cleft%281.002%5Cright%29%5E%7Bk-1%7D%20%20)
The infinite geometric series is converges if |r| < 1.
We have r =1.002 > 1, therefore our infinite geometric series is Diverges
Answer: c. Diverges, sum not exist.
Q.35
![\sum\limits_{k=1}^{\infty}-5\left(\dfrac{4}{5}\right)^{k-1}](https://tex.z-dn.net/?f=%20%20%5Csum%5Climits_%7Bk%3D1%7D%5E%7B%5Cinfty%7D-5%5Cleft%28%5Cdfrac%7B4%7D%7B5%7D%5Cright%29%5E%7Bk-1%7D%20%20)
The infinite geometric series is converges if |r| < 1.
We have r = 4/5 < 1, therefore our infinite geometric series is converges.
The sum S of an infinite geometric series with |r| < 1 is given by the formula :
![S=\dfrac{a_1}{1-r}](https://tex.z-dn.net/?f=S%3D%5Cdfrac%7Ba_1%7D%7B1-r%7D)
We have:
![a_1=-5\left(\dfrac{4}{5}\right)^{1-1}=-5\left(\dfrac{4}{5}\right)^0=-5\\\\r=\dfrac{4}{5}](https://tex.z-dn.net/?f=a_1%3D-5%5Cleft%28%5Cdfrac%7B4%7D%7B5%7D%5Cright%29%5E%7B1-1%7D%3D-5%5Cleft%28%5Cdfrac%7B4%7D%7B5%7D%5Cright%29%5E0%3D-5%5C%5C%5C%5Cr%3D%5Cdfrac%7B4%7D%7B5%7D)
substitute:
![S=\dfrac{-5}{1-\frac{4}{5}}=-\dfrac{5}{\frac{1}{5}}=-5\cdot\dfrac{5}{1}=-25](https://tex.z-dn.net/?f=S%3D%5Cdfrac%7B-5%7D%7B1-%5Cfrac%7B4%7D%7B5%7D%7D%3D-%5Cdfrac%7B5%7D%7B%5Cfrac%7B1%7D%7B5%7D%7D%3D-5%5Ccdot%5Cdfrac%7B5%7D%7B1%7D%3D-25)
Answer: c. Converges, -25.
Answer:
here is your answer
Step-by-step explanation:
b
c
a answer