The radius of convergence R is 1 and the interval of convergence is (-3, -1) for the given power series. This can be obtained by using ratio test.
<h3>Find the radius of convergence R and the interval of convergence:</h3>
Ratio test is the test that is used to find the convergence of the given power series.
First aₙ is noted and then aₙ₊₁ is noted.
For ∑ aₙ, aₙ and aₙ₊₁ is noted.
= β
- If β < 1, then the series converges
- If β > 1, then the series diverges
- If β = 1, then the series inconclusive
Here
=
and
= 
Now limit is taken,
= 
= 
= 
= 
=
< 1
- 1 <
< 1
- 1 - 2 < x < 1 - 2
- 3 < x < - 1
We get that,
interval of convergence = (-3, -1)
radius of convergence R = 1
Hence the radius of convergence R is 1 and the interval of convergence is (-3, -1) for the given power series.
Learn more about radius of convergence here:
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C is the answer
for example
assume that the height of a rectangular prism is 2, width is 1 and length measures 3
the volume will be 6
(2*1*3)
if we multiply height with the scale factor of 1/2
it becomes 1
so the volume will be 3
(1*1*3)
this situation goes for other examples, too
good luck
Answer:
0,4
1,6
2,8
3,10
Step-by-step explanation:
if x=0, 2*0+4=0+4=4
if x=1, 2*1+4=2+4=6
if x=2, 2*2+4=4+4=8
if x=3, 2*3+4=6+4=10
A) On the first place we can put 9 digits, on the second 9, on the third place 8 and on the last place 7 ( because no digits can be repeated ):
9 · 9 · 8 · 7 =4536 numbers
b) There are 5 odd digits can be repeated. So:
5 · 10 · 10 · 5 = 2500 numbers
c) On the first place we can put:5,6,7,8,9 (5 digits) On the last place is just one (0), because the number must be divisible by 10:
5 · 10 · 10 · 1 = 500 numbers
d) on the first place we can put 2 digits ( 1, or 2 - there are no 4-digit numbers starting with 0). The last digit must be even, but the order can be:
X - odd - odd - even 2 · 5 · 4 · 5 = 200
X - odd - even - even 2 · 5 · 5 · 4 = 200
X - even - odd - even 2 · 5 · 5 · 4 = 200
X - even - even - even 2 · 5 · 4 · 3 = 120
Finally: 200+ 200 + 200 + 120 = 720 numbers