Bestimme die folgenden Reihensummen:

  1. ´sum_(n=10)^(oo) (1/2)^n´
  2. ´sum_(n=1)^(oo) (-1)^(n+1) 1/n´
  3. ´sum_(n=0)^(oo) (-1)^n 1/(2n+1)´
Approach
  1. ´sum_(n=10)^(oo) (1/2)^n = 1/1024 + 1/2048 + 1/4096 + … = 1/512´
  2. ´sum_(n=1)^(oo) (-1)^(n+1) 1/n = 1 - 1/2 + 1/4 - 1/8 + 1/16 - … = ln(2)´
  3. ´sum_(n=0)^(oo) (-1)^n 1/(2n+1) = 1 - 1/3 + 1/5 - 1/7 + … = pi/4´

Solution
    1. ´1/512´
    2. ´ln(2)´
    3. ´pi/4´
  • URL:
  • Language:
  • Subjects: math
  • Type: Calculate
  • Duration: 30min
  • Credits: 3
  • Difficulty: 0.6
  • Tags: hpi series
  • Note:
    HPI, 2014-05-05, Mathe 2, Aufgabe 18
  • Created By: adius
  • Created At:
    2014-07-26 10:10:11 UTC
  • Last Modified:
    2014-07-26 10:10:11 UTC