Ask Question
20 March, 11:04

Write out the first eight terms of the series to show how the series starts. Then find the sum of the series or show that it diverges.

Summation from n equals 1 to infinity left parenthesis 2 minus StartFraction 3 Over 4 Superscript n EndFraction right parenthesis

+2
Answers (1)
  1. 20 March, 14:44
    0
    The first right terms are

    5/4, 13/8, 7/4, 29/16, 37/20, 15/8, 53/28, 61/32.

    And the series is divergent.

    Step-by-step explanation:

    Given the series

    S = ∑ (2 - 3/4n) from n = 1 to infinity

    For n = 1

    S1 = 2 - 3/4 = 5/4

    S2 = 2 - 3/8 = 13/8

    S3 = 2 - 3/12 = 7/4

    S4 = 2 - 3/16 = 29/16

    S5 = 2 - 3/20 = 37/20

    S6 = 2 - 3/24 = 15/8

    S7 = 2 - 3/28 = 53/28

    S8 = 2 - 3/32 = 61/32

    So, the first 8 terms are:

    5/4, 13/8, 7/4, 29/16, 37/20, 15/8, 53/28, 61/32.

    Let us show that it diverges.

    Let R = lim (a_n) as n - --> infinity

    a_n = 2 - 3/4n

    R = lim (2 - 3/4n) as n - -> infinity.

    R = 2 - 0 = 2

    Since R ≠ 0, we conclude that the series is divergent.
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “Write out the first eight terms of the series to show how the series starts. Then find the sum of the series or show that it diverges. ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers