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Find the sum of the first n terms

  1. Apr 25, 2014 #1
    1. The problem statement, all variables and given/known data

    Find the sum of the first n terms of the sequence U1, U2, U3...... Ur

    2. Relevant equations



    3. The attempt at a solution

    $$ \sum_{r = 1}^n (1 + (-1)^r) = n + (-1)^n $$

    But I don't this is right... any help?
     
  2. jcsd
  3. Apr 25, 2014 #2

    Mark44

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    What are U1, U2, etc.?
     
  4. Apr 25, 2014 #3
    It doesn't say this is the exact question, it just wants me to find the Sum of the first n terms of this case
     
  5. Apr 25, 2014 #4

    SammyS

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    Like before, write out the first few terms of the series.
     
  6. Apr 25, 2014 #5
    It alternates between 1 and -1 so would the sum would alternate between -1 and 0... so... 1/2( (-1)^n -1) ?
     
  7. Apr 25, 2014 #6

    SammyS

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    You said, "It" alternates ...

    What is the "It" you refer to?

    The series never decreases.


    Write out the first several terms of the sequence, then the first several terms of the series.
     
  8. Apr 25, 2014 #7
    when I mean "it" I meant the sequence. I'm sorry and what I typed above was in reference to the part I did not understand, the sum of (-1)^n. I understand the sum of 1 to n terms = n.

    so my final answer is $$ n + 1/2((-1)^n -1)$$
     
  9. Apr 25, 2014 #8

    SammyS

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    That looks pretty good.

    S1 = 0

    S2 = 2

    S3 = 2

    S4 = 4

    S5 = 4

    ...
     
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