Chapter 11B

Question 1

binomial series formula

Answer 1

(1+x)^k= series n=0 to infinity (kn)x^n

Question 2

(kn)= (for binomial series)

Answer 2

(k(k-1)(k-2)…(k-n+1))/n!

Question 3

power series representations

Answer 3

f(x)= series n=0 to infinity x^n

Question 4

taylor series

Answer 4

f(x)= series n=0 to infinity f of n (a)/n! times (x-a)^n

Question 5

maclaurin series

Answer 5

a=0, series n=0 to infinity f of n (0)/n! times x^n

Question 6

Taylor’s Inequality (Remainder Theorem)

Answer 6

use smaller range for x, bigger number for the absolute value (ex: instead of x-1)
formula: absolute value of Rn(x) is < or equal to abs value of f^n+1/(n+1)! times absolute value of (x-a)^n+1

Question 7

ratio test

Answer 7

lim as n–>infinity absolute value of (an+1/an)

Question 8

for interval of convergence:

Answer 8

convergent: bracket, included
divergent: parentheses, not included