EXAMPLE 5 Express 1/(1 − x)2 as a power series by differentiating the equation below. What is the radius of convergence? 1 1 − x = 1 + x + x2 + x3 + = [infinity] xn n = 0 |x| < 1 SOLUTION Differentiating each side of the equation, we get 1 (1 − x)2 = 1 + Correct: Your answer is correct. + 3x2 + = [infinity] n = 1 . If we wish, we can replace n by n + 1 and write the answer as 1 (1 − x)2 = [infinity] n = 0 . According to this theorem, the radius of convergence of the differentiated series is the same as the radius of convergence of the original series, namely, R = .

in 4 days he will run   12/14

step-by-step explanation:

question:

could we have options?

8

step-by-step explanation:

to find the amount of gift bags to use all the supplies, find the gcf or greatest common factor. this is the largest number which multiplies evenly into each term.

48 has factors: 1, 2, 3, 4, 6, 8, 12. 16, 24, 48

80 has factors: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

64 has factors: 1, 2, 4, 8, 8, 16, 32, 64

the highest number factor they all share in common is 8. this means there will be 8 bags with 6 pencils, 10 markers, and 8 stickers in each bag.

rick has $1400 and sally has $1500

step-by-step explanation:

to find amount of money rick has after 10 years :

principal = $1000 , time = 10 years , rate = 4% annually

to find amount of money sally has after 10 years :

her friend gives to pay her $50 per year, therefore money she has after 10 years = 50 × 10 = $500

also, sally gets $1000 after 10 years,

therefore, total amount of money sally has after 10 years = 500 + 1000 = $1500

so, after 10 years : rick has $1400 and sally has $1500