Results 1 to 2 of 2

Math Help - Recursive to Sum if possible

  1. #1
    MHF Contributor
    Joined
    Mar 2010
    From
    Florida
    Posts
    3,093
    Thanks
    5

    Recursive to Sum if possible

    Given the following recursive definition is it possible to write it as a sum?

    \displaystyle a_0=1,337,101.43 \ \ \ a_n=a_{n-1}(1+33*.02)*1.03^{n-1}
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,693
    Thanks
    1466
    So x_n= (1.66)(1.03)^{n-1}a_{n-1}?

    My suggestion would be to calculate some of them:
    a_1= (1.6)a_0
    a_2= (1.6)(1.03)a_1= (1.6)^2(1.03)a_0
    a_3= (1.6)(1.03)^2a_2= (1.6)^3(1.03)^3a_0
    a_4= (1.6)(1.03)^3a_3= (1.6)^4(1.03)^6a_0
    a_5= (1.6)(1.03)^4a_4= (1.6)^5(1.03)10a_0
    etc.

    So it's clear that the formula involves (1.6)^{n-1}. The powers on 1.03 are 0, 1, 1+ 2= 3, 1+ 2+ 3= 6, 1+ 2+ 3+ 4= 10, etc. for n= 1, 2, 3, 4, 5, ... That is, of course, \frac{n(n- 1)}{2}.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. recursive
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: May 26th 2010, 05:27 PM
  2. Look at the recursive
    Posted in the Differential Geometry Forum
    Replies: 6
    Last Post: February 14th 2010, 04:24 AM
  3. Recursive!!! Am I doing this right??
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: March 21st 2009, 08:10 PM
  4. Primitive Recursive vs Recursive Functions
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: January 29th 2009, 07:32 AM
  5. recursive def
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: July 31st 2007, 08:01 AM

Search Tags


/mathhelpforum @mathhelpforum