(n+1)! <100000 how do i find n?

  • #1
hangainlover
83
0

Homework Statement


(n+1)! <100000 how do i find n?


Homework Equations





The Attempt at a Solution


I can find it by plugging it into the calculator
but i want to do it analytically.
Thanks
 

Answers and Replies

  • #3
Hurkyl
Staff Emeritus
Science Advisor
Gold Member
14,950
19
I can find it by plugging it into the calculator
but i want to do it analytically.
Why? :confused:
 
  • #4
36,191
8,172
I agree with Hurkyl. Just do it by trial and error using a calculator.
 
  • #5
icystrike
446
1
You should be expecting something really small for n.
Sometimes you have to take a little time to meditate on the question before you start(considering what approach you want to take and by your intuition will it lead you to anywhere).

Thus, if you work it out ,

0! = 1 By def[tex]^{n}[/tex]
1! = 1
2! = 2
3! = 3x2 = 6
4! = 4x3x2 = 24 (realizing that its slightly smaller than the factor 25 of 10,000)
5! = 5x4x3x2 = 5x24 < 400x25 = 10,000
6! = 6x5x4x3x2 = 30x24 < 400x25 = 10,000
7! = 210x24 < 400x25 = 10,000
8! = 1680 x 24 ( you realise that one of the factor is way larger than 400 and another is smaller than 24 , inconclusive)

Consider using a factor larger than 25 ... how about 26? 2x13 .. we have yet to reach 13! , analogously you will choose 28 as your choice.

8! = 4x360x28 > 2x200x25 = 10,000


Now you may draw a conclusion.
 
Last edited:
  • #6
dacruick
1,039
1
divide both sides by a factorial. 100000/ ! = n +1. n = 100000/! - 1.
 
  • #7
icystrike
446
1
divide both sides by a factorial. 100000/ ! = n +1. n = 100000/! - 1.

What operation is that?
 
  • #9
fedderenator
15
0
LMAO divide both sides by a factorial....wow...
 

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