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Find the sum to n terms

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

    Wn = 2 + 3(1/2)^n

    2. Relevant equations



    3. The attempt at a solution

    I am confused, all I tried so far is writing out the first 5 terms, but all that was helping me to do is basically find the Sum to infinity... so what should I do to find the Sum to n terms? I know the 3(1/2)^n will be a g.p. , and the 2 makes it sort of an ap.
     
  2. jcsd
  3. Apr 25, 2014 #2

    Mark44

    Staff: Mentor

    Since n is going to be a parameter representing the number of terms, it shouldn't also be an index for the individual terms, so write you sequence as Wk = 2 + 3(1/2)k.

    Now, since you want the sum of the first n terms, your summation looks like this:
    $$ \sum_{k = 1}^n (2 + 3(1/2)^k)$$

    What properties of summations do you know?
     
  4. Apr 25, 2014 #3
    I can separate the sums , $$ \sum_{k = 1}^n (2 )$$ and $$ \sum_{k = 1}^n (3(1/2)^k)$$

    I'm not sure how to separate the latter, never seen one with an index before, well I don't recall..
     
  5. Apr 25, 2014 #4
    Try writing a few terms out and notice what you can do with all the 3s that appear. Do you recall the Geometric Series?
     
  6. Apr 25, 2014 #5
    I could sum the 3s separately?,Oh and then just replace the SUm of the (1/2)^k with the basic geometric sum formula?

    so the Sn = 2n + 3n + a(1-(1/2)^n/[1-1/2] ?
     
    Last edited: Apr 25, 2014
  7. Apr 25, 2014 #6
    nevermind I got it to be 2N + 3(1-2^-N)
     
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