Results 1 to 5 of 5

Math Help - Progression question

  1. #1
    Junior Member
    Joined
    Feb 2011
    Posts
    56

    Progression question

    Find the value of the following series: i need help with (h). Thanks in advance... Progression question-dsc00555.jpg
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Quote Originally Posted by MichaelLight View Post
    Find the value of the following series: i need help with (h). Thanks in advance... Click image for larger version. 

Name:	DSC00555.jpg 
Views:	13 
Size:	427.2 KB 
ID:	21016

    \displaystyle{\sum\limits^{10}_{r=1}\left(4r+\left  (\frac{16}{5}\right)^r\right)=4\sum\limits^{10}_{r  =1}r+\sum\limits^{10}_{r=1}\left(\frac{16}{5}\righ  t)^r , and now the hints:

    1) For any \displaystyle{n\in\mathbb{N}\,,\,\,\sum\limits^n_{  k=1}k=\frac{n(n+1)}{2}} ;

    2) for any \displaystyle{1\neq a\in\mathbb{R}\,,\,n\in\mathbb{N}\,,\,\,\sum\limit  s^n_{k=1}a^k=\frac{a^{n+1}-1}{a-1}}

    Now solve your problem (h)...

    Tonio
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Feb 2011
    Posts
    56
    Quote Originally Posted by tonio View Post
    \displaystyle{\sum\limits^{10}_{r=1}\left(4r+\left  (\frac{16}{5}\right)^r\right)=4\sum\limits^{10}_{r  =1}r+\sum\limits^{10}_{r=1}\left(\frac{16}{5}\righ  t)^r , and now the hints:

    1) For any \displaystyle{n\in\mathbb{N}\,,\,\,\sum\limits^n_{  k=1}k=\frac{n(n+1)}{2}} ;

    2) for any \displaystyle{1\neq a\in\mathbb{R}\,,\,n\in\mathbb{N}\,,\,\,\sum\limit  s^n_{k=1}a^k=\frac{a^{n+1}-1}{a-1}}

    Now solve your problem (h)...

    Tonio
    Thanks for your reply. From the two formulas you provided above, only (1) looks familiar to me, as for the (2), is it possible for you to prove it (i.e. how to obtain that formula..)? Thanks....
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Quote Originally Posted by MichaelLight View Post
    Thanks for your reply. From the two formulas you provided above, only (1) looks familiar to me, as for the (2), is it possible for you to prove it (i.e. how to obtain that formula..)? Thanks....

    Google "geometric progression" or "geometric sequence"

    Tonio
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Apr 2005
    Posts
    14,971
    Thanks
    1121
    Or "geometric series".
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. progression question
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: November 22nd 2010, 03:17 AM
  2. Question about geometric progression
    Posted in the Calculus Forum
    Replies: 2
    Last Post: August 25th 2009, 08:57 AM
  3. question on progression
    Posted in the Algebra Forum
    Replies: 3
    Last Post: May 30th 2008, 08:25 PM
  4. Question on geometric progression
    Posted in the Algebra Forum
    Replies: 1
    Last Post: April 26th 2008, 07:07 PM
  5. Arithmetic Progression question
    Posted in the Algebra Forum
    Replies: 5
    Last Post: September 2nd 2006, 03:16 AM

Search Tags


/mathhelpforum @mathhelpforum