Math

posted by .

Show that the series cos(n) from n=1 to infinity is divergent.

  • Math -

    The sum of the series ∑cos(nx) is, according to Mathworld,
    N
    ∑cos(nx) = cos(Nx/2)sin((N+1)x/2) / sin(x/2)
    n=0
    (Note that the summation starts from 0, make adjustments accordingly).
    The given series has x=1, or
    S(1)=∑cos(n)

    We see that the sum to N oscillates as N increases. Since we cannot find a value of N for whcih |T(n+1)|/|T(n)|<1 ∀n>N , we conclude that the series does not converge.

    I make a difference between divergence where the sum approaches ±∞ and where the sum oscillates. I call the latter non-convergent.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    For what values of p>0 does the series Riemann Sum [n=1 to infinity] 1/ [n(ln n) (ln(ln n))^p] converge and for what values does it diverge?
  2. calculus

    is this correct? use the integral test to determine if this series is convergent or divergent: the series from n=2 to infinity of 1/(n*square root of (ln(n))) I said it was divergent because the integral went to infinity
  3. calculus

    Determine whether the series is convergent o divergent and say what test you used to solve it. (d) sum n=1 to infinity (5n)^(3n) / (5^n + 3)^n (e) sum k=1 to infinity 5 / sqr(2k - 1)
  4. Calc 2

    Is the series convergent or divergent? n=1 series to infinity (-1)^n * (sqrt(n)/(4+5sqrt(n)) Does this diverge?
  5. Calculus

    Is the series 2/ln(n) convergent or divergent?
  6. Calculus 2 (Series - Convergent or Divergent?)

    Can someone show me a step by step process and explanation how to solve this problem?
  7. Integral Calculus - Series

    Find if series is convergent or divergent. Series from n=2 to infinity (4n+7)/(3n^3 -8n)
  8. Calc 2

    Determine whether the series is convergent or divergent series symbol n=1 to infinity (n^2/(e^(3n))
  9. Calculus II

    I need to find if the summation of (n^4)/(n^10 + 1) is convergent or divergent from n=1 to infinity. I tried splitting it up into two sums, one being 1/n^6, which would be convergent because p=6>1, and then the other being n^4, …
  10. Calculus

    The divergence test applied to the series ∑n=1 to ∞ 3n/(8n+9) tells us that the series converges or diverges?

More Similar Questions