Answer:
c
Step-by-step explanation:
Given that:
![\sum \limits ^{\infty}_{k=1} \dfrac{kcos (k\pi)}{k^3+2}](https://tex.z-dn.net/?f=%5Csum%20%5Climits%20%5E%7B%5Cinfty%7D_%7Bk%3D1%7D%20%5Cdfrac%7Bkcos%20%28k%5Cpi%29%7D%7Bk%5E3%2B2%7D)
since cos (kπ) = ![-1^k](https://tex.z-dn.net/?f=-1%5Ek)
Then, the series can be expressed as:
![\sum \limits ^{\infty}_{k=1} \dfrac{(-1)^kk)}{k^3+2}](https://tex.z-dn.net/?f=%5Csum%20%5Climits%20%5E%7B%5Cinfty%7D_%7Bk%3D1%7D%20%5Cdfrac%7B%28-1%29%5Ekk%29%7D%7Bk%5E3%2B2%7D)
In the sum of an alternating series, the best bound on the remainder for the approximation is related to its
term.
∴
![\sum \limits ^{\infty}_{k=1} \dfrac{(-1)^{(3+1)}(3+1))}{(3+1)^3+2}](https://tex.z-dn.net/?f=%5Csum%20%5Climits%20%5E%7B%5Cinfty%7D_%7Bk%3D1%7D%20%5Cdfrac%7B%28-1%29%5E%7B%283%2B1%29%7D%283%2B1%29%29%7D%7B%283%2B1%29%5E3%2B2%7D)
![\sum \limits ^{\infty}_{k=1} \dfrac{(-1)^{(4)}(4))}{(4)^3+2}](https://tex.z-dn.net/?f=%5Csum%20%5Climits%20%5E%7B%5Cinfty%7D_%7Bk%3D1%7D%20%5Cdfrac%7B%28-1%29%5E%7B%284%29%7D%284%29%29%7D%7B%284%29%5E3%2B2%7D)
![= \dfrac{4}{64+2}](https://tex.z-dn.net/?f=%3D%20%5Cdfrac%7B4%7D%7B64%2B2%7D)
![=\dfrac{2}{33}](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B2%7D%7B33%7D)
Answer:
Step-by-step explanation:
It's hard to tell what you mean. I'm going to assume you mean that you want what is left to be 3/7 less.
1400 - 3/7 1400 = 1400 - 600 = 800
Answer:
C
btw Hannah is this one fine? sorry i couldn't remember which question was the chat and sorry i couldn't respond right away im not the person who is on late in the day
Step-by-step explanation:
Answer: -1
Step-by-step explanation:
-8 (-8x - 6) = -6x - 22
distribute
64x + 48 = -6x -22
get rid of the smallest x by adding 6x to both side
70x + 48 = -22
minus 48 to both sides
70x = -70
divide both side by 70
x = -1
Where's the "triangle with alt. BD?" This problem can be solved without the diagram, but the solution would be easier with it.
BD is the altitude. Find the length of BD by finding the dist. between (-1,4) and (2,4); it is 2-(-1), or 3. |BD| = 3.
I've graphed the triangle myself and have found that the "base" of the triangle is the vertical line thru (2,1) and (2,6); its length is 6-1, or 5.
Thus, the area of this triangle is A = (b)(h) / 2, or A = (5)(3) / 2 = 10/3 square inches.