CALC 2

Let an = Hn - ln(n), where Hn is the nth harmonic number
Hn = 1 + 1/2 + .... + 1/n

a. Show that an > 0 for n>= 1 (Hint: show Hn >= integral from 1 to n+1 dx/x)
b. Show {an} is decreasing by interpreting an - an+1 as a positive area. (Hint: use the previous part)
c. Prove lim n-> infinity an exists

Any help is much appreciated. Thank you!!

  1. 👍 0
  2. 👎 0
  3. 👁 231

Respond to this Question

First Name

Your Response

Similar Questions

  1. MATH

    the fist term of a geometric series is 1, the nth term is 128 and the sum of the n term is 225. Find the common ratio and the number of terms?

  2. Physics

    A distance of 5.00 cm is measured between two adjacent nodes of a standing wave on a 20.0 cm long string. A) In which harmonic number is the string vibrating?

  3. Harmonic Oscillation

    The velocity of a certain simple harmonic oscillator is given by: v=-(12m/s)sin [(6.0rad/s)t]. What is the amplitudeof the simple harmonic oscillator. Please show your work.

  4. Difficult Trig Word Problem

    The displacement of a spring vibrating in damped harmonic motion is given by y(t) = 4e^-3t sin(2pi*t) where y = displacement and t = time with t greater than/equal to zero. Find the time(s) when the spring is at its equilibrium

  1. physics

    Which one of the following statements about standing waves on a string is FALSE? Select one: a. All other frequencies are integer multiples of the first harmonic b. The first harmonic is the lowest frequency standing wave that can

  2. Physics

    A distance of 5.00 cm is measured between two adjacent nodes of a standing wave on a 20.0 cm long string. A) In which harmonic number is the string vibrating? B) Find the frequency of this harmonic if the string has a mass of 1.75

  3. Algebra 1 Honors

    Write an equation for the nth term of the arithmetic sequence. Then graph the first five terms in the Sequence. -3,-8,-13,-18 I got 5n-8 as my formula. Then plugged 5 in for n and got 17 for the 5th number in the sequence. Is this

  4. physics

    Suppose a diving board with no one on it bounces up and down in a simple harmonic motion with a frequency of 3.00 Hz. The board has an effective mass of 10.0 kg. What is the frequency of the simple harmonic motion of a 62.0 kg

  1. PHYSICS

    A variable length air column (closed on one end) is placed just below a vibrating wire of mass 5.00g, which is fixed at both ends. The length of the air column is gradually increased from zero until the first position of resonance

  2. Calculus 2 - Series

    I am so confused on how to do series problems...especially these. How can you tell the pattern and determining the formula for them? Can someone please help? 26) Write the first five terms of the sequence {an} whose nth term is

  3. Math

    Find 2 numbers whose arithmetic mean exceeds their geometric mean by 2and whose harmonic mean is 1/5 of the larger number

  4. Algebra

    Reposting: The geometric mean and arithmetic mean of the two numbers are 8 and 17 respectively. 1. find the bigger number 2. find the smaller number 3. find the harmonic mean Thanks in advance to whoever will answer :)

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