The
-th term
in the series is evidently
![\dfrac{2n-1}{(2n-1)!} = \dfrac{2n-1}{(2n-1)(2n-2)!} = \dfrac1{(2n-2)!}](https://tex.z-dn.net/?f=%5Cdfrac%7B2n-1%7D%7B%282n-1%29%21%7D%20%3D%20%5Cdfrac%7B2n-1%7D%7B%282n-1%29%282n-2%29%21%7D%20%3D%20%5Cdfrac1%7B%282n-2%29%21%7D)
By the ratio test, the infinite series converges, since
![\displaystyle \lim_{n\to\infty} \left| \frac{\frac1{(2(n+1)-2)!}}{\frac1{(2n-2)!}}\right| = \lim_{n\to\infty} \frac{(2n-2)!}{(2n)!} = \lim_{n\to\infty} \frac1{2n(2n-1)} = 0 < 1](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bn%5Cto%5Cinfty%7D%20%5Cleft%7C%20%5Cfrac%7B%5Cfrac1%7B%282%28n%2B1%29-2%29%21%7D%7D%7B%5Cfrac1%7B%282n-2%29%21%7D%7D%5Cright%7C%20%3D%20%5Clim_%7Bn%5Cto%5Cinfty%7D%20%5Cfrac%7B%282n-2%29%21%7D%7B%282n%29%21%7D%20%3D%20%5Clim_%7Bn%5Cto%5Cinfty%7D%20%5Cfrac1%7B2n%282n-1%29%7D%20%3D%200%20%3C%201)
Answer:
The variable that needs to be eliminated in these systems of equations are 3x
Step-by-step explanation:
-3x + 4y = -50
3x + 3y = -6
*solve from top to bottom, if that makes sense, so add 3x to -3x, 4y to 3y, and -50 to -6.*
0 + 7y = -56
7y = -56
*divide by 7 to get y alone*
y = -8
plug y into one of the original equations to get x
-3x + 4y = -50
-3x + 4(-8) = -50
-3x - 32 = -50
+32 +32
-3x = -18
x = 6
Answer:
<h2>10.3seconds</h2>
Step-by-step explanation:
Step one:
given data
acceleration,a= 10ft/sec^2
final velocity v= 70mph
first, let is convert mph to ft/sec
1mph is 1.46667 ft/sec
70 mph is x
cross multiply we have
x= 102.7ft/s
Step two:
we are using the first equation of motion
v=u+at
initial velocity u= 0m/s
102.7=0+10*t
102.7=10t
divide both sides by 10
t=10.3seconds
Answer: one angle would be 50 degrees while the other would be 130 degrees.
Step-by-step explanation:
Answer:
0.06 and to change that to a percentage all you do is move the decimal point 2 places to the right so the answer would be <u>6</u><u> </u>percent