Results 1 to 3 of 3

Math Help - Mathematical Induction

  1. #1
    Member
    Joined
    Apr 2008
    Posts
    107

    Mathematical Induction

    Theres a quiz tomorrow and i have never felt soo lost.. please explain well every step.. thank you so much

    Show that the following statemnet is true for all natural numbers n.

    1 + 3 + 5 + ...+ (2n - 1 ) = n^2
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by NeedHelp18 View Post
    Theres a quiz tomorrow and i have never felt soo lost.. please explain well every step.. thank you so much

    Show that the following statemnet is true for all natural numbers n.

    1 + 3 + 5 + ...+ (2n - 1 ) = n^2
    see problem 1 in the attachment (I found it using google by the way. this is a standard problem)
    Attached Files Attached Files
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    13
    I'll assume that you've ever seen this symbol: \sum.

    -----

    Start with the base case n=1 and prove that it's true. Now, let's assume our proposition for n=k, hence, it follows that \sum\limits_{i=1}^{k}{(2i-1)}=k^{2}. We need to prove that \sum\limits_{i=1}^{k+1}{(2i-1)}=(k+1)^{2}. Here's the proof:

    \begin{aligned}<br />
   \sum\limits_{i=1}^{k+1}{(2i-1)}&=\sum\limits_{i=1}^{k}{(2i-1)}+\sum\limits_{i=k+1}^{k+1}{(2i-1)} \\ <br />
 & =k^{2}+2k+1 \\ <br />
 & =(k+1)^{2}.\quad\blacksquare <br />
\end{aligned}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Mathematical Induction
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: August 31st 2010, 04:31 PM
  2. Mathematical induction
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: August 30th 2010, 06:54 AM
  3. Replies: 10
    Last Post: June 29th 2010, 01:10 PM
  4. mathematical induction
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: April 13th 2009, 06:29 PM
  5. Mathematical Induction
    Posted in the Algebra Forum
    Replies: 1
    Last Post: March 18th 2009, 09:35 AM

Search Tags


/mathhelpforum @mathhelpforum