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butalik [34]
3 years ago
15

Find the radius of convergence, R, of the series. ∞ (−1)n (x − 6)n 4n + 1 n = 0 R =

Mathematics
1 answer:
Rina8888 [55]3 years ago
3 0

I'm guessing the series is

\displaystyle\sum_{n=0}^\infty\frac{(-1)^n(x-6)^n}{4n+1}

Use the ratio test: we have

\displaystyle\lim_{n\to\infty}\left|\frac{\frac{(-1)^{n+1}(x-6)^{n+1}}{4n+5}}{\frac{(-1)^n(x-6)^n}{4n+1}}\right|=|x-6|\lim_{n\to\infty}\left|\frac{4n+1}{4n+5}\right|=|x-6|

The series converges for

|x-6|

which has a radius of convergence of 1.

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HELPPP!!! WILL MARK BRAINLIEST!!!
LenKa [72]

Answer:

Horizontal Asymptote:    y=2

Vertical Asymptote: x=3

Step-by-step explanation:

One way: Look at graph

Look at for a horizontal or vertical line that both lines don't touch.

Second Way:

When you look for vertical asymptotes, you set the denominator equal to zero and solve.

For example, the second question has a denominator of x-3.

x-3=0

x=3 (This is the vertical asymptote)

When you look for horizontal asymptote, you do long division.

For example, the first question f(x)=\frac{2x}{x-3}

The answer will be 2. 2 is the quotient. You only want quotient not remainder.

y=2.

6 0
2 years ago
In a box there are 21 identical pieces that have been enumerated using odd numbers from 5 to 45. How many tiles should be drawn
Orlov [11]

These are the only combinations of exactly 3 tiles that add to 33.

5,7,21

5,9,19

5,11,17

5,13,15

7,9,17

7,11,15

9,11,13

All tiles with numbers above 21 do not help you. 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45. There are 12 of them.

Every three-number combination must have one of the numbers 5, 7, or 9, so if the six numbers from 13 to 21 are picked, in addition to the 12 higher numbers mentioned above, you already picked 18 tiles, and you still have no solution. To obtain the solutions 5,7,21; 5,9,19; 7,9,17; he needs two more numbers in addition to the 18 he already has, so he needs 20 tiles in total to be guaranteed three of them add to exactly 33.

Answer: 20 tiles

4 0
3 years ago
Use the functions to find x
suter [353]

Answer:

x = 14

Step-by-step explanation:

f(x) = 10 -  \frac{9}{2} x \\  \\ plug \: f(x) =  - 53 \\  \\  - 53 = 10 -  \frac{9}{2} x \\  \\ \frac{9}{2} x  = 10 + 53 \\  \\ \frac{9}{2} x  = 63 \\  \\ x = 63 \times  \frac{2}{9}  \\  \\ x = 7 \times 2 \\  \\ x = 14

5 0
3 years ago
What is the prudct of 7/9and 6 A. 1 4\9 B. 3 7\9 C. 4 2\3 D. 7 5\7
weeeeeb [17]

Answer:

14/3

Step-by-step explanation:

7/9*6

= 14/3

Hope it helps you

7 0
3 years ago
What scale factor was applied to the large rocket to produce the small rocket? Show your work and clearly mark your final answer
Kryger [21]

Answer:80

Step-by-step explanation:

6 0
3 years ago
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