Important Maclaurin Series

Question 1

1/1-x

Answer 1

Sum from 0-infinity of x^n =1+x+x^2+x^3

R=1

Question 2

e^x

Answer 2

Sum from 0-infinity of x^n/n!=1+x/1!+x^2/2!+x^3/3!

R=infinity

Question 3

sinx

Answer 3

Sum from 0-infinity of (-1)^n*x^2n+1/(2n+1)!=x-x/3!+x^5/5!

R=infinity

Question 4

cosx

Answer 4

Sum from 0-infinity of (-1)^n*x^2n/(2n)!=1-x^2/2!+x^4/4!-x^6/6!
R=infinity

Question 5

arctanx

Answer 5

Sum from 0-infinity of (-1)^n*x^2n+1/2n+1=x-x^3/3+x^5/5

R=1

Question 6

ln(1+x)

Answer 6

Sum from 1 to infinity of (-1)^n-1*x^n/n=x-x^2/2+x^3/3-x^4/4

R=1

Question 7

(1+x)^k

Answer 7

Sum from 0 to infinity of (k n)x^n=1+kk+k(k-1)/2!x^2+k(k-1)(k-2)/3!*x^3
R=1