Answer:
R must lie between the two values 4 and 7
R ∈ (4,7)
Step-by-step explanation:
∑[tex]C_{n}[/tex][tex](x+4)^{n}[/tex]
converges at x= 0 and Diverges at x= -11
Given series is centered at x= -4
since the series converges at x= 0, which is a distance of 4 from x= -4
=> the radius of convergence (R) is at least 4
since the series diverges at x= -11, which is a distance of 7 from x= -4
=> the radius of convergence (R) cannot be more than 7
=> 4 ≤ R ≤ 9 ⇒ R ∈ (4,7)
Following are the calculation of the value that lie on R:
Given:
[tex]\Sigma C_n(x+4)^{n}[/tex]
converges at [tex]x=0[/tex]
diverges at [tex]x=-11[/tex]
To find:
Find the value of R that lie=?
Solution:
[tex]\to \bold{\Sigma C_n(x+4)^{n}}[/tex]
When
[tex]x=0\\\\\to (0)+4=4\\\\\to R \geq 4\\\\[/tex]
When
[tex]\to x=-11\\\\\to (-11)+4=-7\\\\\to R \leq -7[/tex]
So,
[tex]\bold{R \in \ [4,-7]}[/tex]
Therefore, the answer is "[tex]\bold{R \in \ [4,-7]}[/tex]".
Learn more:
brainly.com/question/13026849
