Calculus

posted by .

Find a series ∑a_n for which ∑(a_n)^2 converges but ∑|a_n| diverges

  • Calculus -

    Consider
    1 - 1/2 + 1/3 - 1/4 + ... (alternating harmonic series)


    1 + 1/4 + 1/9 + 1/16 + ... = π2/6


    1 + 1/2 + 1/3 + 1/4 + ... diverges (harmonic series)

  • Calculus -

    thanks!!

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. statistics

    I'm trying to work through the proof for SST = SSM + SSE MEAN = ∑(X)/N SST = ∑((x - MEAN)^2) = ∑(x^2 - 2 * x1 * MEAN + MEAN^2) = ∑(x^2) - 2 * MEAN * ∑(x) + N * MEAN^2 = ∑(x^2) - 2 * ∑(x)^2/N …
  2. math

    -Write the arithmetic sequence 21,13,5,-3... in the standard form: a_n= -a_n=a_1+(n-1)d--so a_n=21+(n-1)-8 *a_n=-168-8n why isnt this right?
  3. Calculus

    If a_n >0 and b_n >0 and series ∑ sqrt( (a_n)^2 +(b_n)^2 ) converges, then ∑a_n and ∑b_n both converge. True or false?
  4. Calculus

    If a_n does not equal zero for any n>=1 and ∑a_n converges absolutely, then ∑ 1/|a_n| diverges. The series are from n=1 to infinity. I think this is true but I'm not sure.
  5. Calculus

    If a_n>0 and a_(n+1) <= a_n, does the alternating series ∑ ((-1)^(n+1)) a_n converge or diverge?
  6. mathematical statistics

    Suppose a_n∈ [0,1] and X_n is a sequence of i.i.d random variables with p.d.f : p(X_n=1)= p(X_n= -1)=0.5 . ∑_(n=1)^∞▒a_n X_n is convergent with probability 1, is ∑_(n=1)^∞▒a_n^2 convergent?
  7. Math

    ∑(x+y) c. ∑(x+∑(y)) d. ∑x+ ∑y e. ∑(x)+ ∑(y)* what do each of these mean?
  8. Calculus 2

    I need help in solving an initial-value problem and a few series problems (Especially on #45 & #46). I don't really understand how to do the series problems...majority of the time. An explanation would be great as well. Thank you for …
  9. Algebra

    For the following sequences determine the term indicated: a_1=-2, a_n=2(a_n-1)^2,a_4 a_n=ln(e^n+2), a_5 b_0=1, b_1=2, b_n+1=2b_n-b_0
  10. DISCRETE MATH

    Determine whether the following is a recursive or explicit. Then, find the first four terms of the following sequence. a) a_n = 〖na〗_(n-1) where a_0 =5 b) a_n = a_(n-1) + 3a_(n-2) where a_0 = 1 and a_1 =2 c) a_n = 2^n …

More Similar Questions