Test 3

Question 1

Binomial series form

Answer 1

(1+x)^k = Σ(k n)(x)^n

Question 2

Geometric series sum

Answer 2

s = (a / (1 - r)) where a is the first term

Question 3

What is the preferred form of testing a series if there are natural logs?

Answer 3

Integral test

Question 4

Conditions for integral test

Answer 4

Positive, continuous, and decreasing

Question 5

Limit comparison test

Answer 5

If f(x) / g(x) is any number and not zero or infinity means they both either diverge or converge

Question 6

Maclaurin Series for
1 / (1 - x)

Answer 6

Σ x^n

Question 7

Maclaurin Series for
e^x

Answer 7

Σ x^n / n!

Question 8

Maclaurin Series for
sin(x)

Answer 8

Σ (-1)^n * (x^(2n+1) / (2n+1)!)

Question 9

Maclaurin Series for
cos(x)

Answer 9

Σ (-1)^n * (x^2n) / (2n)!

Question 10

Maclaurin Series for
arctan(x)

Answer 10

Σ (-1)^n * x^(2n+1) / (2n+1)

Question 11

Maclaurin Series for
ln(1 + x)

Answer 11

(n = 1) Σ (-1)^(n-1) * x^n / n

Question 12

Taylor’s inequality

Answer 12

M / (n + 1)! * |x - a|^(n+1)
Where M is the greatest value on the nth + 1 derivative (f^(n+1)(x))
You also select an a value that makes x - a the greatest value

Question 13

Remainder theorem for A.S.T.

Answer 13

Rn = s - sn <= bn+1

Question 14

(k chus n)

Answer 14

(k!) / (n! * (k - n)!)

Question 15

Chu’s formula patter

Answer 15

k * (k - 1) * (k - 2) n times

Question 16

Remainder estimate using integrals

Answer 16

Rn <= int from n to infinity f(x) dx