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1. [-/4 Points] DETAILS LARCALC119.9.004.

Find a geometric power series for the function, centered at 0, by the following methods.

1

f(x) =

5+x

(a) by the technique shown in Examples 1 and 2

f(x) =

(b) by long division (Give the first three terms.)

f(x) =

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л-0

2. [-/4 Points] DETAILS LARCALC11 9.9.006.

Find a geometric power series for the function, centered at 0, by the following methods.

6

f(x)=

9-x

f(x) =

(a) by the technique shown in Examples 1 and 2

Σ

(b) by long division (Give the first three terms.)

f(x) =

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3. [-/4 Points]

f(x) = Σ

Л-0

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DETAILS LARCALC11 9.9.007.

Find a power series for the function, centered at c.

f(x)=

c=2

Determine the interval of convergence. (Enter your answer using interval notation.)/n4. [-/4 Points] DETAILS

Find a power series for the function, centered at c.

5

2x

C = 4

f(x) =

f(x) =

n=0

Determine the interval of convergence. (Enter your answer using interval notation.)

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5. [-/4 Points]

f(x) =

f(x) =

Find a power series for the function, centered at c.

4

3x + 2

n=0

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g(x) =

DETAILS

Determine the interval of convergence. (Enter your answer using interval notation.)

LARCALC119.9.012.

c=5

6. [-/4 Points] DETAILS

n=0

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LARCALC11 9.9.014.MI.

Find a power series for the function, centered at c.

g(x) =

4x

x²+2x-3

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LARCALC11 9.9.015.

c=0/n7. [-/4 Points]

Find a power series for the function, centered at c.

9

f(x) = Σ

n=0

Determine the interval of convergence. (Enter your answer using interval notation.)

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8. [-/4 Points]

f(x) =

DETAILS LARCALC11 9.9.018.

h(x) =

Use the power series

-

h(x) =

n=0

DETAILS LARCALC11 9.9.019.

to find a power series for the function, centered at 0.

-2

1

2²1

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c=0

Σ(-1), x < 1

n=0

=

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+

Determine the interval of convergence. (Enter your answer using interval notation.)

1

Watch It/n9. [-/4 Points]

Use the power series

f(x) =

n=0

to determine a power series for the function, centered at 0,

п-D

DETAILS

f(x)=

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10. [-/4 Points]

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f(x) =

14

(x + 1)

Determine the interval of convergence. (Enter your answer using interval notation.)

Use the power series

n=0

(-1)"x", |x| < 1

DETAILS

f(x) = In(x + 1) =

LARCALC11 9.9.022.

=

Σ(-1) ²² x < 1

n=0

to find a power series for the function, centered at 0.

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7

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LARCALC11 9.9.023.

-dx

x + 1

Determine the interval of convergence. (Enter your answer using interval notation.)

Watch It/n11. [-/4 Points]

Use the power series

f(x) =

(-1)^² x < 1

л-0

to find a power series for the function, centered at 0.

f(x) = In(x + 1)

Σ

Determine the interval of convergence. (Enter your answer using interval notation.)

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DETAILS

12. [-/4 Points]

f(x) =

Use the power series

Σ

n=0

LARCALC11 9.9.026.

DETAILS LARCALC11 9.9.028.MI.

n=0

to find a power series for the function, centered at 0.

f(x) = arctan 9x

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Σ(-1)^² x < 1

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Determine the interval of convergence. (Enter your answer using interval notation.)

Master It/n13. [-/4 Points]

Use the power series

f(x) =

Σει

to find a power series for the function, centered at 0.

1

f(x) =

(1-x)²

n=1

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Determine the interval of convergence. (Enter your answer using interval notation.)

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14. [-/4 Points]

DETAILS

Use the fact that

(a)

(b)

-

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DETAILS

LARCALC11 9.9.037.

(1-x)"

#Σ (7)" -E

n=1

÷ [-(9)*-[

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Σ nxn-1 to find the sum of each series.

LARCALC11 9.9.042./n15. [-/4 Points]

LARCALC11 9.9.047.

Find the sum of the convergent series by using a well-known function. (Round your answer to four decimal places.)

(−1)″ + 1_

4"n

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16. [-/4 Points]

LARCALC11 9.9.049.

Find the sum of the convergent series by using a well-known function. (Round your answer to four decimal places.)

2n

(-1)+1;

5"n

n=0

DETAILS

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DETAILS

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17. [-/4 Points]

LARCALC11 9.9.051.

Find the sum of the convergent series by using a well-known function. (Round your answer to four decimal places.)

1

(-1) 62n+1(2n +1)

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DETAILS

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Watch It/n18. [-/4 Points]

DETAILS LARCALC11 9.9.052.

Find the sum of the convergent series by using a well-known function. (Round your answer to four decimal places.)

(−1)″ +1-

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19. [-/4 Points]

f(x) = Σ

n=0

Find a power series for the function, centered at c.

5

f(x) =

c=-3

5-x

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1

g2n-1(2n-1)

Determine the interval of convergence. (Enter your answer using interval notation.)

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DETAILS LARCALC11 9.9.501.XP.

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n-06

20. [-/4 Points] DETAILS LARCALC11 9.9.504.XP.

Find the sum of the series. (Round your answer to six decimal places.)

(-1)^2+1

2n +

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*(2n + 1)!

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