Can any1 plz give an ezly understandable proof of how " !n = [n!/e] "?

(Here !n denotes the derangement of n elements and [x] denoted the closest integer to x)

## Search found 25 matches

- Wed Feb 04, 2015 4:40 pm
- Forum: Higher Secondary Level
- Topic: Looking for a proof: ! n = [n!/e]
- Replies:
**1** - Views:
**1266**

- Wed Feb 04, 2015 4:33 pm
- Forum: Higher Secondary Level
- Topic: Where did the other root go?
- Replies:
**7** - Views:
**2641**

### Re: Where did the other root go?

Sorry didn't see it

- Tue Feb 03, 2015 12:01 am
- Forum: College / University Level
- Topic: Integrability
- Replies:
**3** - Views:
**4391**

### Re: Integrability

Well.. But can we integrate all discontinuous functions as well??

- Mon Feb 02, 2015 11:57 pm
- Forum: Higher Secondary Level
- Topic: Where did the other root go?
- Replies:
**7** - Views:
**2641**

### Re: Where did the other root go?

Replace x by -x in the equation, and -x by x. Do u see any change?Nirjhor wrote:Then how is $-\ln\left(1+\sqrt 2\right)$ another root?

- Thu Jan 29, 2015 9:34 pm
- Forum: Higher Secondary Level
- Topic: Need help
- Replies:
**3** - Views:
**1887**

### Re: Need help

I think the ques. shud be "the product of n non-negative numbers is maximum when and only when all the numbers are equal provided that their sum is a constant" Let us suppose the statement to be P(n) for natural number n. We will show the following: P(2) is true, P(n) is true implies P(2n) is true, ...

- Thu Jan 29, 2015 8:32 pm
- Forum: Higher Secondary Level
- Topic: Infinity*zero= ??
- Replies:
**5** - Views:
**2419**

### Re: Infinity*zero= ??

The answer of question no.(1) will be 0 and question no.(2) will be infinity I don't think infinity^0=0. Can u explain how? Besides, as we define the index 0, infinity^0=infinity/infinity, which does not seem to make any sense unless u define how the infinity is reached (i also think that infinity ...

- Thu Jan 29, 2015 8:06 pm
- Forum: Higher Secondary Level
- Topic: Where did the other root go?
- Replies:
**7** - Views:
**2641**

### Re: Where did the other root go?

Sorry, i made a mistake.. Correcting it below:

$\frac{e^{x}-e^{-x}}{2}=1$

$\Rightarrow e^{x}-e^{-x}=2$

$\Rightarrow e^{2x}-2e^{x}-1=0$

$\Rightarrow e^{x}=1\pm \sqrt{2}$

$\frac{e^{x}-e^{-x}}{2}=1$

$\Rightarrow e^{x}-e^{-x}=2$

$\Rightarrow e^{2x}-2e^{x}-1=0$

$\Rightarrow e^{x}=1\pm \sqrt{2}$

**The rest part follows now...**- Mon Jan 26, 2015 2:39 pm
- Forum: Higher Secondary Level
- Topic: Where did the other root go?
- Replies:
**7** - Views:
**2641**

### Where did the other root go?

Let's solve the equation: $\frac{e^{x}+e^{-x}}{2}=1$ $\Rightarrow e^{x}+e^{-x}=2$ $\Rightarrow e^{2x}-2e^{x}+1=0$ $\Rightarrow e^{x}=1\pm \sqrt{2}$ But $e^{x }$ cannot be negative, so $x= ln (1+ \sqrt {2}) \approx 0.881$ But from the equation, it is clearly observable that $-0.881$ is an approx root...

- Thu Jan 22, 2015 4:10 pm
- Forum: College / University Level
- Topic: Integrability
- Replies:
**3** - Views:
**4391**

### Integrability

(1) A function is not differentiable at a point if it is not continuous at that point or it is a corner point(that is L.H.S derivative and R.H.S derivative differ in value). What are all the cases in which a function doesn't have (a)an indefinite integral or (b)a definite integral? (2) How do we ev...

- Wed Jan 14, 2015 9:48 pm
- Forum: Higher Secondary Level
- Topic: Looking for projective geometry books
- Replies:
**6** - Views:
**7800**

### Re: Looking for projective geometry books

Thanks. That was helpful