Search found 327 matches

by sm.joty
Tue Aug 28, 2012 12:30 am
Forum: Combinatorics
Topic: Quite hard !!! (may be)
Replies: 4
Views: 2323

Re: Quite hard !!! (may be)

$n!e=n!(1+\frac{1}{2!}+\frac{1}{3!}+...)=(\displaystyle\sum_{k=0}^{n}\frac{n!}{(n-k)!})+\frac{n!}{(n+1)!}+\frac{n!}{(n+2)!}+...$ All we have got to do next is to show that $\frac{n!}{(n+1)!}+\frac{n!}{(n+2)!}+...=\frac{1}{n+1}+\frac{1}{n+2}...<1$. Can we do that? may be here is a typo (i'm not sure...
by sm.joty
Sun Aug 26, 2012 11:15 pm
Forum: Combinatorics
Topic: Quite hard !!! (may be)
Replies: 4
Views: 2323

Quite hard !!! (may be)

Show that for $n \in \mathbb{N}$,
$\displaystyle\sum_ {k = 0}^{n} n \mathrm{P}_k = \left\lfloor{n!e}\right\rfloor $

Source: The Collage Math J.20(1989),260
:ugeek:
by sm.joty
Thu Aug 09, 2012 12:57 pm
Forum: Asian Pacific Math Olympiad (APMO)
Topic: APMO 1990 (Inequality with Combi)
Replies: 2
Views: 2345

Re: APMO 1990 (Inequality with Combi)

Well here is my solution Let prove a quick lemma Lemma:For finite n element set, the product of $a_{1},a_{2}.......,a_{n}$ taken $k$ at a time is $[a_{1}a_{2}.......a_{n}]^{r}$ where $r_{1}=\displaystyle \binom{n-1}{k-1}$ because here every positive integer repeated for $r_{1}$ times. Now back to ma...
by sm.joty
Sun Aug 05, 2012 11:57 am
Forum: International Mathematical Olympiad (IMO)
Topic: IMO 2012: Day 1 Problem 2
Replies: 12
Views: 10269

Re: IMO 2012: Day 1 Problem 2

Hey,nice problem. I also use the similar technique like Tahmid. :D
by sm.joty
Mon Jun 11, 2012 1:03 am
Forum: Secondary Level
Topic: Even,You are odd looking!!!!!!!!!
Replies: 8
Views: 3885

Re: Even,You are odd looking!!!!!!!!!

OOps,not just this part,I think ur solution is totally wrong.Because,After summing, we get,\[10^{16}(x_{1}+x_{17})+10^{15}(x_{2}+x_{16})+10^{14}(x_{3}+x_{15})+...\] Look that,\[(x_{1}+x_{17}),(x_{2}+x_{16}),(x_{3}+x_{15})+...\] can be greater than $9$. So they are not digits(1,2,......9,0) so 1 can...
by sm.joty
Sat Jun 09, 2012 6:43 pm
Forum: Secondary Level
Topic: Even,You are odd looking!!!!!!!!!
Replies: 8
Views: 3885

Re: Even,You are odd looking!!!!!!!!!

Hey,No one interested :? ??? That's very easy one so may be no one want to make a reply. Anyway there is a bug in your problem. You said it is a 17 digit number but your $N$ and $M$ representation says they are 19 digit number ;) ok it's not a matter you can also solve it. here is the solve but now...
by sm.joty
Fri Jun 08, 2012 2:30 pm
Forum: Asian Pacific Math Olympiad (APMO)
Topic: APMO-2012 results
Replies: 6
Views: 3496

Re: APMO-2012 results

Finally the official results of APMO are published http://www.mmjp.or.jp/competitions/APMO/ congratulations to Bappa vai for getting Silver;Mugdho vai and Sourav vai for getting Bronze and also Adib and Choton vai for getting honourable mentions. and the overall position of Bangladesh is 19th.Thank...
by sm.joty
Wed Jun 06, 2012 11:06 pm
Forum: Junior Level
Topic: No repeated digits: 100-999
Replies: 8
Views: 4095

Re: No repeated digits: 100-999

Amar ager ans ta vul chilo....tarahura kore koray vul hoiche..keu notice kore nai. :lol: দেখছিলাম কিন্তু রিপ্লাই দেয়ার টাইম পাই নাই। যাইহোক তোমার মেথড টা ঠিকাছে। এটাকে জেনেরালাইজ কর আরও অনেক মজার জিনিস পাবা। আর এইটা নিয়ে আরও জোস প্রব্লম আছে। আমি কোন জায়গায় জানি দিসিলাম। এই ফোরামেই। খুজে দেখ। জো...
by sm.joty
Fri Jun 01, 2012 11:04 pm
Forum: College / University Level
Topic: Dangerous integretion :P
Replies: 5
Views: 4931

Dangerous integretion :P

Please, any one show me the procedure to get the integral of $sin x^{2} dx$ ????
by sm.joty
Sun May 27, 2012 8:40 pm
Forum: Social Lounge
Topic: অভিনন্দন !
Replies: 12
Views: 6145

Re: অভিনন্দন !

#incude<অভিনন্দন.h> int main() { while(scanf==1) { printf("শুভেচ্ছা"); } if (মেডেল==Bronze) { printf("অভিনন্দন"); } if (মেডেল==Silver) { printf("উরাধুরা অভিনন্দন"); } if (মেডেল==Gold) { printf("তোরে আর কি অভিনন্দন দিমু রে পাগলা। তুই তো কোপাইয়া দিসস।"); } return ভালোবাসা; } :lol: :lol: :lol: :lol: :...