Results 1 to 2 of 2

Thread: Sequence, sum of elements

  1. #1
    Newbie
    Joined
    Sep 2011
    Posts
    12

    Sequence, sum of elements

    Hi!

    Could you help me with this assignment?

    What is the sum of $\displaystyle n$ first elements of the sequence $\displaystyle (a_n)$where:

    $\displaystyle a_1=2, a_2=22, a_3=222, ...$ ?

    Thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Mar 2011
    From
    Awetuouncsygg
    Posts
    182
    Thanks
    12

    Re: Sequence, sum of elements

    First you should have tried to find a formula for $\displaystyle a_{n}$. It's easy to observe that:

    $\displaystyle a_{n}=2(10^{n-1}+10^{n-2}+...+10^{1}+10^{0})=2\cdot \frac{10^{n}-1}{10-1}=\frac{2}{9}\cdot (10^{n}-1)$

    Now that you "know" $\displaystyle a_{n}$ it's simpler to calculate the sum:

    $\displaystyle a_{1}+a_{2}+...+a_{n-1}+a_{n}=\frac{2}{9}\left ( 10^{1}+10^{2}+...+10^{n-1}+10^{n} -n\right )=\frac{2}{9}\left ( 10\cdot \frac{10^{n}-1}{10-1} -n \right )$

    $\displaystyle S_{n}=\frac{2}{9}\cdot \frac{10^{n+1}-10-9n}{9}=\frac{2}{81}\cdot \left (10^{n+1}-9n-10 \right )$

    Pretty clear I hope...
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: Mar 7th 2012, 05:38 PM
  2. Replies: 8
    Last Post: Nov 27th 2011, 10:18 PM
  3. Sequence of the positive elements in B(H)
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: Apr 1st 2011, 05:39 AM
  4. [SOLVED] Limit of a Sequence of Elements in L^2
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: Aug 1st 2010, 11:46 AM
  5. Definition of a sequence of elements in a set?
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: Apr 5th 2007, 11:11 AM

Search Tags


/mathhelpforum @mathhelpforum