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Homework Help: Find a formula for 1, 3, 6, 10, 15, 21,

  1. Jul 18, 2010 #1
    1. The problem statement, all variables and given/known data

    find the formula for

    1,3,6,10,15,21,...

    2. Relevant equations

    n/a

    3. The attempt at a solution

    i only can find n>=3

    Tn = 3 + [tex]\sum[/tex] i ; i=3 to n

    help T_T
     
  2. jcsd
  3. Jul 18, 2010 #2
    Re: Series

    For one thing, the numbers in the way you listed them are called a sequence. Do you see a pattern among those numbers? That may help you.
     
    Last edited: Jul 18, 2010
  4. Jul 18, 2010 #3
    Re: Series

    yea lol, it's sequence ;P sorry, and yea, i saw the pattern, but only start from 3 T_T
     
  5. Jul 18, 2010 #4

    HallsofIvy

    User Avatar
    Science Advisor

    Re: Series

    But 3= 1+ 2 and 1= 0+ 1 so you can say it is [itex]T_n= \sum_{i= 1}^n i[/itex] That's a well known sum with a well known formula. Look up "triangular numbers".

     
  6. Jul 18, 2010 #5
    Re: Series

    thanks, how come i didn't realised it's [itex]T_n= \sum_{i= 1}^n i[/itex] instead of Tn = 3 + sum(i) ; i=3 to n.

    thank you :D
     
  7. Jul 18, 2010 #6
    Re: Series

    There is no sigma notation in sequences, a sequence is written as:

    [tex]
    \left \{a_{n} \right \}_{n=0}^{N}
    [/tex]

    as to your sequence it could be defined by a recursive formula:

    [tex]
    a_{n+1}=a_{n}+n+2
    [/tex]

    [tex]
    a_{0}=1
    [/tex]
     
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