Consider the sequence {an}={1/2n}.   The first five terms in this sequence are what. Enter a comma separated list of numbers (in order).   The first five partial sums of this sequence are  what. Enter a comma separated list of numbers (in order).   The sum of the first n terms of the sequence is the partial sum Sn=1/2+1/4+1/8+⋯+1/2n= ? . Your answer should be in terms of n.   The sum of all terms in the sequence is defined as the the limit of the partial sums, which means what?   Select all true statements (there may be more than one correct answer): A. The sequence converges to 0. B. The sequence converges to 1. C. The limit of the sequence of partial sums is 0. D. The limit of the sequence of partial sums is 1. E. The series converges to 0. F. The series converges to 1.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question

Consider the sequence {an}={1/2n}.

 
    1. The first five terms in this sequence are what. Enter a comma separated list of numbers (in order).
 
    1. The first five partial sums of this sequence are  what. Enter a comma separated list of numbers (in order).
 
    1. The sum of the first n terms of the sequence is the partial sum Sn=1/2+1/4+1/8+⋯+1/2n= ? . Your answer should be in terms of n.
 
    1. The sum of all terms in the sequence is defined as the the limit of the partial sums, which means what?
 
  1. Select all true statements (there may be more than one correct answer):
    A. The sequence converges to 0.
    B. The sequence converges to 1.
    C. The limit of the sequence of partial sums is 0.
    D. The limit of the sequence of partial sums is 1.
    E. The series converges to 0.
    F. The series converges to 1.
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