calculus

posted by .

The sum from n=1 to infinity of cos(npi/3)/n!

Does this absolutely converge, conditionally converge, or diverge?

  • calculus -

    Group every 6 terms (1 cycle) together and consider as an aggregate term for a new series, ΣQn. Assume that all the terms are positive because of the n! in the denominator.

    If you can prove that
    Qn+1/Qn < 1, then
    by the ratio test, the (new) series is absolutely convergent.

    Can you take it from here?

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    for what values of x does the series converge absolutely and for what values does it converge conditionally?
  2. Calculus

    For the sequences below, find if they converge or diverge. If they converge, find the limit. an=(3^(n+2))/(5^n) an=cos(2/n) an=(2^(1+3n))^1/n I am unsure about how to get started on these problems so some assistance would be great.
  3. calculus

    Does the series from 0 to infinity of [1/square root of (n+4)] x cos(n x pi) converge or diverge?
  4. Calculus 2

    n=1 series to infinity (-5^n)/n^3 does it absolutely converge, diverge or conditionally converge. Would I be applying the ratio test?
  5. Calc 2

    How would I do this one? n=1 to infinity n^n/4^1+3*n Does it absolutely converge, conditionally converge, or diverge?
  6. Calculus II

    Does 3/(2^(n) +1) diverge or converge in an infinite sum?
  7. Calculus

    does the sum 3/(2^(n)-1) converge or diverge?
  8. Calculus-PLZ HELP! =)

    does the sum 3/(2^(n)-1) converge or diverge?
  9. Calculus

    does the sum e^n / n! converge or diverge?
  10. Calculus

    does the series 1/(n^2+n) converge or diverge?

More Similar Questions