- #1

- 83

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## 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

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- Thread starter hangainlover
- Start date

- #1

- 83

- 0

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

I can find it by plugging it into the calculator

but i want to do it analytically.

Thanks

- #2

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- 2

- #3

Hurkyl

Staff Emeritus

Science Advisor

Gold Member

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Why?I can find it by plugging it into the calculator

but i want to do it analytically.

- #4

Mark44

Mentor

- 34,884

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I agree with Hurkyl. Just do it by trial and error using a calculator.

- #5

- 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.

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

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divide both sides by a factorial. 100000/ ! = n +1. n = 100000/! - 1.

- #7

- 446

- 1

divide both sides by a factorial. 100000/ ! = n +1. n = 100000/! - 1.

What operation is that?

- #8

Mark44

Mentor

- 34,884

- 6,621

This makes no sense at all.divide both sides by a factorial. 100000/ ! = n +1. n = 100000/! - 1.

- #9

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LMAO divide both sides by a factorial....wow...

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