Results 1 to 13 of 13

Math Help - [SOLVED] series

  1. #1
    Member ronaldo_07's Avatar
    Joined
    Nov 2008
    Posts
    175

    [SOLVED] series

    1,3,7,15,31 I need a forumlae to fit that series please
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member MacstersUndead's Avatar
    Joined
    Jan 2009
    Posts
    291
    Thanks
    32
    {a_1}= 1 and a(n + 1) = {a_n} + 2^n I think work. I'm a bit sleepy
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member ronaldo_07's Avatar
    Joined
    Nov 2008
    Posts
    175
    That is not the formulae I am looking for. I used that formulae to get these values. also i would like to know how to do part c

    The question is:

    Let a1;a2;a3; : : : be numbers satisfying the rules that a1 = 1 and
    a_n = 2 a_{n {\color{red}-} 1} + 1 for all n > 1.

    (a) Write down the first few numbers an.

    (b) Guess a formula for an.

    (c) Prove your guess by induction.
    Last edited by ronaldo_07; January 13th 2009 at 07:51 PM. Reason: mistake in question
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Oct 2008
    Posts
    12
    2^n - 1

    And n=1

    I'm not sure if this is what you're looking for.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by ronaldo_07 View Post
    That is not the formulae I am looking for. I used that formulae to get these values. also i would like to know how to do part c

    The question is:

    Let a1;a2;a3; : : : be numbers satisfying the rules that a1 = 1 and
    an = 2(an+1) +1 for all n > 1.

    (a) Write down the first few numbers an.

    (b) Guess a formula for an.

    (c) Prove your guess by induction.
    It would have saved time and effort if you'd given this information in the first place.

    And it would help if you gave the correct recurrence relation which I assume is a_n = 2 a_{n {\color{red}-} 1} + 1.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member ronaldo_07's Avatar
    Joined
    Nov 2008
    Posts
    175
    sorry it was a typo

    this infact is what I wanted to show
    a_n = 2 a_{n {\color{red}-} 1} + 1
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by ronaldo_07 View Post
    sorry it was a typo

    this infact is what I wanted to show
    a_n = 2 a_{n {\color{red}-} 1} + 1
    Cakecake has correctly answered (b) in reply #4.

    Where are you stuck with (c)? Please show your working.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Member ronaldo_07's Avatar
    Joined
    Nov 2008
    Posts
    175
    thanks
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Member ronaldo_07's Avatar
    Joined
    Nov 2008
    Posts
    175
    i have substituted the values n=1,2,3,4,5 to show part c is that correct?
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by ronaldo_07 View Post
    i have substituted the values n=1,2,3,4,5 to show part c is that correct?
    No. That's not how proof by induction works. Have you been taught proof by induction?
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Member ronaldo_07's Avatar
    Joined
    Nov 2008
    Posts
    175
    yes but it is very confusing how to approach it.
    Follow Math Help Forum on Facebook and Google+

  12. #12
    Member ronaldo_07's Avatar
    Joined
    Nov 2008
    Posts
    175
    for induction I start off with n=0 and see if it still follows the pattern and in this case it dosen't I think. As this would make 2^0-1 = 0
    Follow Math Help Forum on Facebook and Google+

  13. #13
    MHF Contributor
    Joined
    Mar 2007
    Posts
    1,240

    Talking

    Quote Originally Posted by ronaldo_07 View Post
    yes but it is very confusing how to approach it.
    If you're having trouble figuring out how to use the induction-proof technique, try studying a few online articles until you feel more confident.

    Then return to this exercise and give it another go. If you get stuck, you will then be able to reply with a clear listing of what you have tried and where you are stuck.

    Have fun!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Series
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: May 12th 2010, 08:05 PM
  2. [SOLVED] sum of series
    Posted in the Calculus Forum
    Replies: 5
    Last Post: April 11th 2010, 09:58 PM
  3. [SOLVED] series
    Posted in the Calculus Forum
    Replies: 5
    Last Post: April 7th 2010, 07:12 PM
  4. [SOLVED] Series (p-series)
    Posted in the Calculus Forum
    Replies: 4
    Last Post: December 9th 2009, 10:36 AM
  5. [SOLVED] Sum of Series...
    Posted in the Calculus Forum
    Replies: 4
    Last Post: May 10th 2009, 12:23 PM

Search Tags


/mathhelpforum @mathhelpforum