Things to memorize for final

Question 1

e^x series general term

Answer 1

x^n / n! = 1 + x + x^2/2 + x^3/3!

Question 2

cos(x) series general term

Answer 2

(-1)^n * x^2n / (2n)! = 1 - x^2/2 + x^4/4! - x^6/6!

Question 3

sin(x) series general term

Answer 3

(-1)^n * x^(2n+1) / (2n+1)! = x - x^3/3! + x^5/5! - x^7/7!

Question 4

1/(1-x) series general term

Answer 4

x^n = 1 + x + x^2 + x^3 (geometric series)

Question 5

ln(1+x) series general term

Answer 5

(-1)^(n+1) * x^n/n = x - x^2/2 + X^3/3 - x^4/4. (keep in mind that this series is taken from the derivative and that the first term is x)