1. Questions

Calculus

Determine the following about the series. Indicate the test that was used and justify your answer.

Sigma (lower index n = 1; upper index infinity) [sin((2n-1)pi/2)]/n

A. The series diverges
B. The series converges conditionally.
C. The series converges absolutely.
D. It cannot be determined.

  1. 👍
  2. 👎
  3. 👁
Jenny

  1. since sin(nth odd multiple of pi/2) = -(-1)^n the sequence is

    1 - 1/2 + 1/3 - 1/4 +...

    The alternating harmonic series converges to ln(2)

    1. 👍
    2. 👎
    Steve

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calc 12

    Let f be the function defined by f(x) = (x^2 + 1)e^-x for -4≤x≤4. a. For what value of x does f reach its absolute maximum? Justify your answer. b. Find the x-coordinates of all points of inflection of f. Justify your answer.

  2. math

    Determine whether QS || PT . Justify your answer. PQ = 18, QR = 6, RS = 12, ST = 36

  3. Calculus

    Consider a differentiable function f having domain all positive real numbers, and for which it is known that f'(x)=(4-x)x^-3 for x>0. A. Find the x-coordinate of the critical point of f. Determine whether the point is a relative

  4. science

    A student thinks she might have accidentally mixed up her sugar and her salt and put them in the wrong containers. The crystals look similar and have no smell. Which test can the student run to determine which one is sugar and

  1. calculus

    Let g be the function give by g(x) = x^4 - 4x^3 + 6x^2 – 4x + k where k is constant. A.On what intervals is g increasing? Justify your answer. B.On what interval is g concave upward? Justify your answer. C.Find the value of k

  2. Statistics

    Teen Communication The following data represent the number of different communication activities (e.g., cell phone, text messaging, e-mail, Internet, and so on) used by a random sample of teenagers over the past 24 hours. (a) Are

  3. calculus

    test the series for convergence or divergence using the alternating series test the sum from n=1 to infinity of (-1)^n/(3n+1) I said it converges, is this true?

  4. Calculus

    Use the Integral test to determine whether the series is convergent or divergent. infinity "series symbol" n=1 (ne^(n"pi")) Note: I don't know how to solve or work out so show all your work. And give the answer in EXACT FORM

  1. Grade 7 Math

    All the numbers from 1 to 99 are multiplied together. Use a pattern to determine the last digit of the product. Justify your answer.

  2. statistics

    Determine whether each of the distributions given below represents a probability distribution. Justify your answer. (A) x 1 2 3 4 P(x) 1/5 5/12 1/3 1/6 (B) x 3 6 8 P(x) 0.2 2/5 0.3 (C) x 20 35 40 50 P(x) 0.3 -0.1 0.5 0.3

  3. Math

    In a geometric series, t1=12 and S3=372. What is the greatest possible value for t5? Justify your answer.

  4. calculus

    determine whether the series converges of diverges the sum from n=1 to infinity of 1/(the square root of (n^3+1)) I said that through the comparision test (comparing to 1/the square root of (n^3) the series converges

You can view more similar questions or ask a new question.