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Summation of 'n' terms of the given expression

  1. Apr 5, 2014 #1
    1. The problem statement, all variables and given/known data

    find the general formula to calculate the sum
    2. Relevant equations

    1+11+111+1111+11111+.............upto n terms

    3. The attempt at a solution

    100 + (101+100) + (102+101 + 100) + (103 + 102+101 + 100) + ................

    ==> (100+100+100+....upto n terms) + (101+101+101+....upto n-1 terms) + (102+102+102+....upto n-2 terms) + .............................................+ (10n-2 + 10n-2) + (10n-1)


    ==>n + (101+101+101+....upto n-1 terms) + (102+102+102+....upto n-2 terms) + ...........................+ (10n-2 + 10n-2) + (10n-1)


    after this i don't know how.They seem to resemble geometric series.
     
  2. jcsd
  3. Apr 5, 2014 #2

    LCKurtz

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    Notice that the kth term of that is ##\frac{10^k-1}9##. Does that help?
     
  4. Apr 9, 2014 #3
    in general how do you find the general term?

    how about this series:112+122+132+........
    GENERAL TERM:n2 ,where n>10;nεN.

    am i right?
     
  5. Apr 9, 2014 #4

    Mark44

    Staff: Mentor

    Yes, that's the general term. The series can be written as a summation like so:
    $$ \sum_{k = 11}^{\infty}k^2$$
     
  6. Apr 9, 2014 #5

    Ray Vickson

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    This is horribly divergent. However, ##\sum_{k=11}^N k^2## is meaningful for any finite ##N##.
     
  7. Apr 9, 2014 #6
    In your first post, you noted that each term seems to resemble a geometric series. Not only does it seem to resemble a gerometric series. That's exactly what each of the terms is. The sum of a geometric series is (arn-a)/(r-1). In your case, a = 1 and r = 10. That's how to get the general term that LCKurtz presented.

    Chet
     
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