Unit 8 - Power Series Expansions

Question 1

e^x

Answer 1

n=0 ∑ (x^n) / (n!)

Question 2

cos(x)

Answer 2

n=0 ∑ (-1)^n * (x^2n) / (2n)!

Question 3

sin(x)

Answer 3

n=0 ∑(-1)^n * (x^2n+1) / (2n+1)!

Question 4

1/(1-x)

Answer 4

n=0 ∑ x^n

Question 5

1/(1+x)

Answer 5

n=0 ∑ (-x)^n

Question 6

tan-1(x)

Answer 6

n=0 ∑ (-1)^n * (x^2n+1) / (2n+1)

Question 7

ln(1+x)

Answer 7

n=1 ∑ (-1)^n+1 * (x^n)/n