Results 1 to 4 of 4

Math Help - equation involving addition of powers

  1. #1
    Member Jskid's Avatar
    Joined
    Jul 2010
    Posts
    160

    equation involving addition of powers

    Show that 2^k+2^k-1=2^{k+1}-1
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,553
    Thanks
    1424

    Re: equation involving addition of powers

    Quote Originally Posted by Jskid View Post
    Show that 2^k+2^k-1=2^{k+1}-1
    \displaystyle \begin{align*} 2^k + 2^k - 1 &= 2\cdot 2^k - 1 \\ &= 2^1 \cdot 2^k - 1 \\ &= 2^{k + 1} - 1  \end{align*}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member Jskid's Avatar
    Joined
    Jul 2010
    Posts
    160

    Re: equation involving addition of powers

    Quote Originally Posted by Prove It View Post
    \displaystyle \begin{align*} 2^k + 2^k - 1 &= 2\cdot 2^k - 1 \\ &= 2^1 \cdot 2^k - 1 \\ &= 2^{k + 1} - 1  \end{align*}
    The very first equality is not apparent to me.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,553
    Thanks
    1424

    Re: equation involving addition of powers

    Quote Originally Posted by Jskid View Post
    The very first equality is not apparent to me.
    n + n = 2n

    Here your n just happens to be 2^k.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Simplifying quotients involving powers of e
    Posted in the Algebra Forum
    Replies: 4
    Last Post: August 14th 2011, 08:27 AM
  2. [SOLVED] Integrals Involving Powers of Trig Functions.
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 28th 2010, 12:26 AM
  3. [SOLVED] Inequality involving added powers
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: September 29th 2010, 12:10 PM
  4. Arithmetic involving powers.
    Posted in the Algebra Forum
    Replies: 1
    Last Post: May 18th 2010, 09:20 PM
  5. Functions involving powers of logarithms
    Posted in the Pre-Calculus Forum
    Replies: 8
    Last Post: August 15th 2009, 06:19 AM

Search Tags


/mathhelpforum @mathhelpforum