Power Series

Question 1

What is the interval of convergence for 1/(1-x)

Answer 1

(-1, 1)

Question 2

What is the interval of convergence for e^x

Answer 2

(-∞, ∞)

Question 3

What is the interval of convergence for sin(x)

Answer 3

(-∞, ∞)

Question 4

What is the interval of convergence for cos(x)

Answer 4

(-∞, ∞)

Question 5

What is the interval of convergence for tan^-1(x)

Answer 5

[-1, 1]

Question 6

What is the interval of convergence for ln(1+x)

Answer 6

(-1, 1]

Question 7

What is the sigma notation for 1/(1-x)

Answer 7

Σ^∞_n=0(xⁿ)

Question 8

What is the sigma notation for e^x

Answer 8

Σ^∞_n=0(xⁿ/n!)

Question 9

What is the sigma notation for sin(x)

Answer 9

Σ^∞_n=0((-1)ⁿx²ⁿ⁺¹/(2n+1)!)

Question 10

What is the sigma notation for cos(x)

Answer 10

Σ^∞_n=0((-1)ⁿx²ⁿ/(2n)!)

Question 11

What is the sigma notation for tan^-1(x)

Answer 11

Σ^∞_n=0((-1)ⁿx²ⁿ⁺¹/(2n+1))

Question 12

What is the sigma notation for ln(1+x)

Answer 12

Σ^∞_n=1((-1)ⁿ⁺¹xⁿ/n)

Question 13

What are the first four terms of the maclaurin series for 1/(1-x)

Answer 13

1 + x + x² + x³

Question 14

What are the first four terms of the maclaurin series for e^x

Answer 14

1 + x/1! + x²/2! + x³/3!

Question 15

What are the first four terms of the maclaurin series for sin(x)

Answer 15

x - x³/3! + x⁵/5! - x⁷/7!

Question 16

What are the first four terms of the maclaurin series for cos(x)

Answer 16

1 - x²/2! + x⁴/4! - x⁶/6!

Question 17

What are the first four terms of the maclaurin series for tan^-1(x)

Answer 17

x - x³/3 + x⁵/5 - x⁷/7

Question 18

What are the first four terms of the maclaurin series for ln(1+x)

Answer 18

x - x²/2 + x³/3 - x⁴/4

Question 19

What series can be written as this using sigma notation:

Σ^∞_n=0(xⁿ)

Answer 19

1/(1-x)

Question 20

What series can be written as this using sigma notation:

Σ^∞_n=0(xⁿ/n!)

Answer 20

e^x

Question 21

What series can be written as this using sigma notation:

Σ^∞_n=0((-1)ⁿx²ⁿ⁺¹/(2n+1)!)

Answer 21

sin(x)

Question 22

What series can be written as this using sigma notation:

Σ^∞_n=0((-1)ⁿx²ⁿ/(2n)!)

Answer 22

cos(x)

Question 23

What series can be written as this using sigma notation:

Σ^∞_n=0((-1)ⁿx²ⁿ⁺¹/(2n+1))

Answer 23

tan^-1(x)

Question 24

What series can be written as this using sigma notation:

Σ^∞_n=0((-1)ⁿ⁺¹xⁿ/n)

Answer 24

ln(1+x)

Question 25

delete this card later pls

Answer 25

idk

Question 25

What maclaurin series starts with these four terms:

1 + x + x² + x³

Answer 25

1/(1-x)

Question 26

What maclaurin series starts with these four terms:

1 + x/1! + x²/2! + x³/3!

Answer 26

e^x

Question 26

What maclaurin series starts with these four terms:

1 + x/1! + x²/2! + x³/3!

Answer 26

e^x

Question 27

What maclaurin series starts with these four terms:

x - x³/3! + x⁵/5! - x⁷/7!

Answer 27

sin(x)

Question 27

What maclaurin series starts with these four terms:

x - x³/3! + x⁵/5! - x⁷/7!

Answer 27

sin(x)

Question 28

What maclaurin series starts with these four terms:

1 - x²/2! + x⁴/4! - x⁶/6!

Answer 28

cos(x)

Question 29

What maclaurin series starts with these four terms:

1 - x²/2! + x⁴/4! - x⁶/6!

Answer 29

cos(x)

Question 30

What maclaurin series starts with these four terms:

x - x³/3 + x⁵/5 - x⁷/7

Answer 30

tan^-1(x)

Question 31

What maclaurin series starts with these four terms:

x - x³/3 + x⁵/5 - x⁷/7

Answer 31

tan^-1(x)

Question 32

What maclaurin series starts with these four terms:

x - x²/2 + x³/3 - x⁴/4

Answer 32

ln(1+x)

Question 33

Which series have this interval of convergence:

(-1, 1)

Answer 33

1/(1-x)

Question 34

Which series have this interval of convergence:

(-∞, ∞)

Answer 34

e^x, sin(x), cos(x)

Question 35

Which series have this interval of convergence:

[-1, 1]

Answer 35

tan^-1(x)

Question 36

Which series have this interval of convergence:

(-1, 1]

Answer 36

ln(1+x)