Results 1 to 4 of 4
Like Tree1Thanks
  • 1 Post By emakarov

Math Help - Find the Last Five Digits

  1. #1
    Newbie
    Joined
    May 2012
    From
    New Delhi
    Posts
    2

    Find the Last Five Digits

    Please help me do this question.

    Find the last five digits of

    (101^100) -1
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jun 2009
    Posts
    658
    Thanks
    131

    Re: Find the Last Five Digits

    10000

    Use the binomial expansion for (1+100)^{100}.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    May 2012
    From
    New Delhi
    Posts
    2

    Re: Find the Last Five Digits

    Dear Sir thank you for your consideration.
    But how would the binomial expansion of the same help as then I would have to add all the numbers
    and then get my results.

    Please help and give a proper explanation if possible.

    Regards
    aakgoel
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,502
    Thanks
    765

    Re: Find the Last Five Digits

    (1 + 100)^{100} - 1 = \binom{100}{1}100+\binom{100}{2}100^2+\binom{100}{  3}100^3+\dots. All terms starting from the third one end with at least 6 zeros, so you need to consider the first two terms only.
    Thanks from Goku
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. find the last two digits
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: March 25th 2011, 08:26 AM
  2. Replies: 0
    Last Post: January 16th 2011, 01:49 PM
  3. Find the last six digits of...
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: October 17th 2008, 06:13 PM
  4. Find sum of the digits of B?
    Posted in the Number Theory Forum
    Replies: 10
    Last Post: August 15th 2008, 08:04 PM
  5. Replies: 2
    Last Post: April 3rd 2007, 12:31 PM

Search Tags


/mathhelpforum @mathhelpforum