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Homework Help: Please explain this limit problem

  1. Dec 20, 2017 #1
    • OP warned about not using the homework template
    Please explain the above limit problem.i am able to understand last steps but cant get initial 4 steps.

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  2. jcsd
  3. Dec 20, 2017 #2


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    The sum of natural numbers 1 to N. Is that the part you are confused about?
    Let's do an example. Say you want to add the numbers 1 to 10. You can group them: Take the first number and the last number (1 + 10) then 2nd number and next to last (2 + 9), then (3 + 8) etc. Each grouping adds to 11 {N+1}. There are 5 groupings {N/2}. So in general, we have (N + 1) * (N/2). This works with odd N values as well.
    Last edited: Dec 20, 2017
  4. Dec 20, 2017 #3
    This trick is something interesting to know about. I will remember it.appreciate your help :smile::smile:
  5. Dec 20, 2017 #4
    But of you look at the 4th step they replaced 'n' by n-1 ..how do that work?
  6. Dec 20, 2017 #5


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    The comment appears to be misplaced. The replacement occurs one step above, going from ##\sum_{r=1}^n## to ##\sum_{r=1}^{n-1}##.
  7. Dec 20, 2017 #6
    Oh i got it. :)
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