math chapter 9 test

Question 0

1/1+x series

Answer 0

1 - x + x^2 - x^3 … (-x)^n

Question 1

1/1-x series

Answer 1

1 + x + x^2 + x^3 … x^n

Question 2

e^x series

Answer 2

1 + x + x^2/2! + x^3/3! … x^n/n!

Question 3

sinx series

Answer 3

x - x^3/3! + x^5/5! … (-1)^n•x^2n+1/(2n+1)!

Question 4

cosx series

Answer 4

1 - x^2/2! + x^4/4! … (-1)^n• x^2n/(2n)!

Question 5

ln(x+1) series

Answer 5

x - x^2/2 + x^3/3 … (-1)^n•x^n+1/(n+1)

Question 6

p test

Answer 6

a to infinity: converges if a is positive and p>1

0 to a: converges if a is positive and 0<p<1

Question 7

ratio test

Answer 7

limit as n -> infinity of an+1/an = r

if -1<r<1, series converges

Question 8

Lagrange remainder

Answer 8

|f(x)-Pn(x)| = Rn(x) < fn+1(c)(x-a)^n+1 / (n+1)!

Question 9

alternating series test

Answer 9

series must be alternating and the limit as n approaches infinity of |an| must be 0, series converges

Question 10

alternating harmonic series

Answer 10

converges to ln2

Question 11

harmonic series

Answer 11

diverges

Question 12

absolute convergence

Answer 12

convergence does not depend on if the series alternates (converges either way)

Question 13

conditional convergence

Answer 13

convergence depends on if the series alternates (if it didn’t alternate, it would diverge)

ex: alternating harmonic