AP Calculus BC

Review for Quiz- Determining convergence of geometric series

- Creating a power series- Finding a Taylor Series sum expression

Question 1

For the series below: Write the first 4 terms of the series, then find the sum that the series converges to.

Solution Q1

1. 5 + 5/4 + 5/16 + 5/64 converges to 20/3

Question 2

Find the power series expression for

Then use your result to find a power series representation for

Solution Q2

And

Question 3

Determine the fourth order Taylor series and the summation equation for f(x) = 1/x when the center is at x = -1

Solution Q3

= - 1 – (x+1) - -

Question 4

• Tell whether each converges or diverges, if it converges give its sum

a.b. + . . . . .

c. x - + - + . . . .

∑𝑛=1

∞

3( 12 )𝑛−1

Q4 key

a. Converges to 6b. Converges to 2/3 (r = -1/2)c. Divergesd. Sin x

Question 5

Find the interval of convergence and the function of x represented by the geometric series

Q5 key

• The interval of convergence is – 1 < x < 3

• And f(x) =

Question 6

Find the interval of convergence and the function of x represented by the geometric series

Q6 key

• f(x) =

• And interval of convergence is (1,5)

Question 7

Find first four terms of the Taylor polynomial for y =

Q7 key

= 1 + (2x) +

Question 8

Find the 5th partial sum and also what the series converges to.

Q8 Key

5th partial sum is

= = 13.02469

Converges to: 15