1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

2017 times a is a natural number

  1. Dec 16, 2016 #1
    1. The problem statement, all variables and given/known data

    category=5.png
    find 2017 times A
    2. Relevant equations


    3. The attempt at a solution
    the sum of last members denominator.is 2017 multiplied by 1008
    the member before it is 2015 multiplied by 1008
    before it 2015 times 1007
    2013 times 1007
    2013 times 2016
    how can i move futher
     
  2. jcsd
  3. Dec 16, 2016 #2

    fresh_42

    Staff: Mentor

    Have you tried to write this equation in summation notation? The denominators can be written in a closed form, which the inverse can be taken of.
     
  4. Dec 16, 2016 #3

    $$A = {1 \over 1+ 2} + {1 \over 1+ 2 +3 } +\cdots + {1 \over 1+ 2+ \cdots +2016}$$
    $$\color {red}{A + 1 = {1\over 1} + {1 \over 1+ 2} + {1 \over 1+ 2 +3 } +\cdots + {1 \over 1+ 2+ \cdots +2016}+ \cdots }$$

    Find the nth term of 'red thing', then do partial fraction decomposition. You will a series that is very easy to compute.
     
  5. Dec 16, 2016 #4

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    A good first step is to try to spot the pattern. With just one term, it is 1/3. What is the sum of the first two? Of the first three?...
     
  6. Dec 16, 2016 #5

    Vanadium 50

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor

    Haruspex has a good hint. A related hint is "about how big do you expect your answer to be?"
     
  7. Dec 17, 2016 #6
    Just one reminder, I guess you have been taught that ##1+2+...+k=\frac{k(k+1)}{2}##, because it should be easy to recognize that, but you don't even mention it in your post or at relevant equations.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: 2017 times a is a natural number
  1. Nature of this number (Replies: 13)

  2. Natural number (Replies: 35)

Loading...