Frequently Used MacLaurin Series

Question 1

1/(1-x)

Answer 1

∑x^k, for ∣x∣ < 1

Question 2

e^x

Answer 2

∑(x^k)/(k!), for ∣x∣ < ∞

Question 3

sinx

Answer 3

∑[(-1)^kx^2k+1]/[(2k+1)!], for ∣x∣ < ∞

Question 4

cosx

Answer 4

[(-1)^kx2k] / [(2k)!] , for ∣x∣ < ∞

Question 5

tan^-1x

Answer 5

∑[(-1)^kx^2k+1] / [2k+1] , for ∣x∣ ≤ 1