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!

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]
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook