I need help on these questions:

Evaluate the geometric series or state that it diverges. M 8 n=0 7+1 Does the series converge or diverge? If it converges, what is its sum? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The series converges. Its sum is . (Type an integer or a simplified fraction.) O B. The series diverges.Use the Alternating Series Test to determine whether the series converges. 2 (- 1) * + 1 k k = 1 10k + 1 Let ax represent the magnitude of the terms of the given series and f(x) be the function that generates a . Determine whether the terms of the series are nonincreasing in magnitude. Select the correct choice below and fill in the answer box in your choice. O A. The terms of the series are nonincreasing in magnitude. Since f'(x) = | 1 8 50 the terms ax decrease for k 2 1. O B. The terms of the series are increasing in magnitude. Since f'(x) = |> 0 for x> 150 the terms a increase for k 2 1.a. Find the linear approximationg polynomial for the following function centered at the given point a. b. Find the quadratic approximationg polynomial for the following function centered at the given point a. c. Use the polynomials obtained in parts a. and b. to approximate the given quantity. f(x) = x", a=1; approximate 0.51/3 a. p1 (x) =Given several terms of a sequence any , complete parts a. through c. below. (6, 8, 10, 12, 14, ..} a. Find the next two terms of the sequence. The next two terms are a; = 16 and a7 = 18 . b. Find a recurrence relation that generates the sequence (supply the initial value of the index and the first term of the sequence). Choose the correct answer below. O A. an+ 1 = an - 2, a1 = 6 for n 2 1 OB. an + 1 = 2 an a, = 6 for n 2 1 c. an + 1 = an + 2, a, =6 for n2 1 O D. an + 1 = 2an, a1 = 6 for n2 1 c. Find an explicit formula for the general, or nth, term of the sequence. an = ,n21