1. Dec 20, 2017 #1

   rishi kesh

   

   • 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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   rishi kesh, Dec 20, 2017
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3. Dec 20, 2017 #2

   scottdave

   

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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

   scottdave, Dec 20, 2017
4. Dec 20, 2017 #3

   rishi kesh

   

   This trick is something interesting to know about. I will remember it.appreciate your help

    

   rishi kesh, Dec 20, 2017
5. Dec 20, 2017 #4

   rishi kesh

   

   But of you look at the 4th step they replaced 'n' by n-1 ..how do that work?

    

   rishi kesh, Dec 20, 2017
6. Dec 20, 2017 #5

   DrClaude

   

   Staff: Mentor

   The comment appears to be misplaced. The replacement occurs one step above, going from ##\sum_{r=1}^n## to ##\sum_{r=1}^{n-1}##.

    

   DrClaude, Dec 20, 2017
7. Dec 20, 2017 #6

   rishi kesh

   

   Oh i got it. :)

    

   rishi kesh, Dec 20, 2017

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