basic mclaurin series

Question 1

1/(1-x)

Answer 1

1+x+x^2+x^3+x^4+…+x^n
IOC: (-1,1)

Question 2

arctanx

Answer 2

x-(x^3/3)+(x^5/5)-(x^7/7)+…+(-1)^n(x^(2n+1)/(2n+1))
IOC: [-1,1]

Question 3

e^x

Answer 3

1+x+(x^2/2!)+(x^3/3!)+(x^4/4!)+…+(x^n/n!)
IOC: (-inf,inf)

Question 4

sinx

Answer 4

x-(x^3/3!)+(x^5/5!)-(x^7/7!)+…+(-1)^n(x^(2n+1)/(2n+1)!)
IOC:(-inf,inf)

Question 5

cosx

Answer 5

1-(x^2/2!)+(x^4/4!)-(x^6/6!)+…+(-1)^n(x^2n/(2n!))
IOC: (-inf,inf)