. The series is divergent. To see this, first observe that the series ∑ 1/kn for n = 1 to ∞ is divergent for any integer k ≥ 2.
Now, if we pick a large integer for k, say k > 100, then for nearly all integers n it will be true that 1 > cos(n) > 1/k. Therefore, since ∑ 1/kn is divergent, ∑ cos(n)/n must also be divergent The *summation* is divergent, but the individual terms converge to the number 0.<span>by comparison test since cosn/n <= 1/n is convergent
and 1/n is divergent by harmonic series
so the series is conditionally converget </span>
Answer:
5a to the power of 2 ofc
Step-by-step explanation:
The most you can make is 16 because you need a dvd in each prize even though there is still pretzels and popcorn
Answer:
48
Step-by-step explanation:
it will travel 48 m in 3 sec
the minute hand is pretty much the radius of the circular clock.
![\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=44 \end{cases}\implies 44=2\pi r\implies \cfrac{44}{2\pi }=r\implies \cfrac{22}{\pi }=r \\\\\\ \stackrel{\textit{using }\pi =\frac{22}{7}}{\cfrac{~~22~~}{\frac{22}{7}}=r}\implies \cfrac{22}{1}\cdot \cfrac{7}{22}=r\implies \cfrac{22}{22}\cdot \cfrac{7}{1}=r\implies 7=r](https://tex.z-dn.net/?f=%20%5Cbf%20%5Ctextit%7Bcircumference%20of%20a%20circle%7D%5C%5C%5C%5C%20C%3D2%5Cpi%20r~~%20%5Cbegin%7Bcases%7D%20r%3Dradius%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20C%3D44%20%5Cend%7Bcases%7D%5Cimplies%2044%3D2%5Cpi%20r%5Cimplies%20%5Ccfrac%7B44%7D%7B2%5Cpi%20%7D%3Dr%5Cimplies%20%5Ccfrac%7B22%7D%7B%5Cpi%20%7D%3Dr%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Busing%20%7D%5Cpi%20%3D%5Cfrac%7B22%7D%7B7%7D%7D%7B%5Ccfrac%7B~~22~~%7D%7B%5Cfrac%7B22%7D%7B7%7D%7D%3Dr%7D%5Cimplies%20%5Ccfrac%7B22%7D%7B1%7D%5Ccdot%20%5Ccfrac%7B7%7D%7B22%7D%3Dr%5Cimplies%20%5Ccfrac%7B22%7D%7B22%7D%5Ccdot%20%5Ccfrac%7B7%7D%7B1%7D%3Dr%5Cimplies%207%3Dr%20)
