Results 1 to 2 of 2

Math Help - deducing a limit...

  1. #1
    Member
    Joined
    Jan 2008
    Posts
    114

    deducing a limit...

    Deduce that \displaystyle\sum_{i=1}^n \frac{1}{n+i}\to log 2 as  n \to \infty

    How on earth do i "deduce this"?! I've tried using  f(x) = \frac{1}{1 + x} but that didn't really get me anywhere...

    Thanks in advance!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    11
    It's a Riemann sum:

    \mathop {\lim }\limits_{n \to \infty } \sum\limits_{i = 1}^n  {\frac{1}<br />
{{n + i}}}  = \mathop {\lim }\limits_{n \to \infty } \frac{1}<br />
{n}\sum\limits_{i = 1}^n  {\frac{1}<br />
{{1 + \dfrac{i}<br />
{n}}}}  = \int_0^1 {\frac{1}<br />
{{1 + x}}\,dx} .

    The rest follows.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 5
    Last Post: May 2nd 2011, 04:16 AM
  2. Help in deducing!
    Posted in the Algebra Forum
    Replies: 1
    Last Post: August 17th 2010, 02:07 AM
  3. Deducing a relation from others
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: April 8th 2010, 09:26 AM
  4. Deducing polynomials technique
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 4th 2010, 03:46 AM
  5. Deducing matrix from minimum polynomial
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: May 12th 2009, 01:40 AM

Search Tags


/mathhelpforum @mathhelpforum