Thursday, April 7, 2011

1!*1 + 2!*2 + 3!*3 + ... + n!*n

1!*1 = 1
1!*1 + 2!*2 = 5
1!*1 + 2!*2 + 3!*3 = 23
1!*1 + 2!*2 + 3!*3 + 4!*4 = 119
1!*1 + 2!*2 + 3!*3 + 4!*4 + 5!*5 = 719
1!*1 + 2!*2 + 3!*3 + 4!*4 + 5!*5 + 6!*6 = 5039

 for n = 1, 2, 3, 4, 5, 6.

Guess the general law, and prove your guess.
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4 comments:

  1. AnonymousApril 7, 2011 at 3:35 PM

    (n+1)! - 1!

    ReplyDelete
  2. AnonymousApril 7, 2011 at 3:42 PM

    for any i: i!*i = (i+1)! - i!
    so sum can be considered as:
    2! - 1! + 3! - 2! ... + n! - (n-1)! + (n+1)! - n! = (n+1)! - 1!

    ReplyDelete
  3. BenVitaleApril 7, 2011 at 9:31 PM

    That's correct.

    ReplyDelete
  4. BenVitaleApril 7, 2011 at 9:31 PM

    Thanks for participating.

    ReplyDelete

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