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Summation of the series

  1. Nov 12, 2012 #1
    S = 12-22+32-42.......+20092

    Attempt=

    S = (1+2)(1-2)+(3+4)(3-4)+.....+(2007-2008)(2007+2008) [can we write this as -(1+2+3+4+5....2008) if yes, then why ?) +20092
    Stuck after this.
     
  2. jcsd
  3. Nov 12, 2012 #2
    Do you know the summation of:
    12+22+32+42+......+n2

    That would be of help here.
     
  4. Nov 12, 2012 #3

    Mentallic

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    Homework Helper

    Yes you can write it as -(1+2+...+2008)+20092 because

    (1+2)(1-2) = -(1+2)
    (3+4)(3-4) = -(3+4)
    ...

    And finally, we factored 20072-20082 but left out the 20092 term so we need to add that term in at the end.

    Now, do you know the formula to sum the first n natural numbers?

    Hint:

    1+2+3+...+(n-2)+(n-1)+n

    = (1+n) + (2+(n-1)) + (3+(n-2))+...
     
  5. Nov 12, 2012 #4
    Just to give you a greater hint to support Mentallic, draw out the numbers from 1 to n
    1+2+3+4....n-3+n-2+n-1+n, now notice, like Mentallic said, how 1+n = n-1+2 = n-2+3, so all those pairs have the same value, and when you have x things with value y, the result is.....



    Bonaparte
     
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