1. |x| < 7 |x| < 1 |x| < 14 |x| < 19
Use the binomial series to expand the function as a power series. Find the radius of convergence. {image}
|x| < 7
|x| < 1
|x| < 14
|x| < 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

2. Use the binomial series to expand the function as a power series
Use the binomial series to expand the function as a power series. Find the radius of convergence. {image}
|x| <1
|x| <6
|x| <7
|x| <3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

3. Use the binomial series to expand {image}1.
{image} 2. 3. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

4. Expand {image} as a binomial series.1.
{image} 2. 3. 4. 5. 6. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

5. The period of a pendulum with length L that makes a maximum angle {image} with the vertical is {image} where {image} and g is the acceleration due to gravity. Use the inequality {image} to estimate to the thousandth the period of a pendulum with L = 1 meter, {image} and g = 9.8.
T = 2.242
T = 2.448
T = 1.466
T = 1.800
T = 2.910
T = 2.018 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50