# គណិតវិទ្យាជុំវិញពិភពលោក(៣)

ចូរបង្ហាញថា$\sum\limits_{n = 1}^{9999} {\left( {{1 \over {\left( {\sqrt n + \sqrt {n+ 1} } \right)\left( {\root 4 \of n + \root 4 \of {n + 1} } \right)}}} \right)} = 9$

ដំណោះស្រាយ

បង្ហាញថា$\sum\limits_{n = 1}^{9999} {\left( {{1 \over {\left( {\sqrt n + \sqrt {n+ 1} } \right)\left( {\root 4 \of n + \root 4 \of {n + 1} } \right)}}} \right)} = 9$

គេមាន$\left( {\root 4 \of {n + 1} + \root 4 \of n } \right)\left( {\root 4\of {n + 1} - \root 4 \of n } \right) = \sqrt {n + 1} - \sqrt n$

$\left( {\root 4 \of {n + 1} + \root 4 \of n } \right)\left( {\root 4\of {n +1} - \root 4 \of n } \right) = {1 \over {\sqrt {n + 1} + \sqrt n }}$

គេទាញ${1 \over {\left( {\sqrt n + \sqrt {n + 1} } \right)\left( {\root 4\of n + \root 4 \of {n + 1} } \right)}} = \root 4\of {n + 1} - \root 4 \of n$

$\sum\limits_{n = 1}^{9999} {\left( {{1 \over {\left( {\sqrt n + \sqrt {n + 1} } \right)\left( {\root 4\of n + \root 4\of {n + 1} } \right)}}} \right) = \sum\limits_{n = 1}^{9999} {\left( {\root 4\of {n + 1} - 1} \right)} }$

$\sum\limits_{n = 1}^{9999} {\left( {\root 4\of {n + 1} - \root 4\of n } \right) = \root 4\of {10000} - 1 = 9}$

ដូចនេះ$\sum\limits_{n = 1}^{9999} {\left( {{1 \over {\left( {\sqrt n + \sqrt {n+ 1} } \right)\left( {\root 4 \of n + \root 4 \of {n + 1} } \right)}}} \right)} = 9$

### 29 responses to “គណិតវិទ្យាជុំវិញពិភពលោក(៣)”

1. jupiter

new style that i never seen. Kool.

• ីI’ll try to post more….if there are readers 😀

• ព្យាយាមឡើងមានអ្នកគាំទ្រច្រើនណាស់!

• 😀 really???thanks for your support!!!I will try all my best to write the greatest math code…

• yeah however u should hire the solution!if someone can’t solve they can look at ur solution.Nice to see ur blog!

• u think I should hide the solution until readers ask for it??? well, I will do 🙂

2. I think u should them both, but the solution in hidden( they can see the solution after they click only) so the readers can solve the exercises or someone just want to read only they will check out ur solution. Just my idea, anyone else will have more good idea to improve ur blog. Good job! ( sorry have mistake in Enlgish written cos I don’t use it for long) 😀

• okay….let see what I can do…and of course, your idea is pretty good…thanks!!!

• I had been thinking hard on how to write “hide until click”html(non-javascript)….but I didn’t make it….so if u know(anyone else) know on how to do this, plz share with me!!!

• I’m not sure how to it but I have a solution, it’s easy just wirte down the exerciese as normal publish it. then U continue write down the solution in another new post.after that save it to draft, next copy the title of that post then use the normaly HTML to hide it ( like u give a link to another site), it’s ok. try it I’ll ask someone who is good at IT for u. 😀 luck

• Uh-huh….good idea!!!thank you very much!!!

• so try it! i think it works cos I do like that too.

• I’m working on it….u helped me a lot!!! 🙂

• yeah i’m the one who always want to help the other but can help as i can only, hehe however i like maths too even i’m not good on it.

• really nice to have u as my friend!!!A friend in need is a friend indeed!!!anyway, m not so good about math too, that’s why I make up this blog to improve myself…are u a scholar of civil engineer in Vietnam??

• yeah I’m in the 4th year in next 2 weeks 🙂 . and u ? where do u study ?

• wow!u must be good at math, physic, and chemistry…about me, m just a high school student who is preparing to attend grade 12 next year 😀

• haha u make me laugh! I’m not good at them at all. but I like to study them so i always try to share my time with them especially Maths. Next year, is ur best time to fight ( to be clever student in Maths and exams at the end of the year ), so try hard and do ur best, Life in High school is my good memory

• ីOh! I see. I’m striving not only for Bac II exam, but to survive for math contest next year too…it’s gonna be tough, tough, and tough…

• yeah good future is waiting for u ! keep going and u will get it soon, I’ll help u if I can I’m not sure how much I can help but by internet and any ideas I used to get from the others. Good luck
However keep update ur blog cos it’s good to help u and share with others. 🙂

• thanks for everything!!! u are just like my teacher__keep giving advices and new ideas… I’ll try to take some time update this blog, and make it a better blog for Khmer students widening their knowledge regarding to math…lolz….m talking like m good at math, but actually not :-Dha ha ha

• hihi u said like this, it looks like i’m too old, hahaha so try another new post for ur blog !

• I didn’t mean u are old…I wanna say u are full of experience…I appreciate that 😉

• hehe just kidding !

3. ហេតុអីក៏ចុច លើដំនោះស្រាយហើយមិនអាចមើលឃើញ?!
សាកល្បងធ្វើសារថ្មីណា!

• ម៉េចចឹង??ខ្ញុំសាកល្បងហើយ ដំណើរការ​បានល្អប្រសើរ!!

• after making a draft of solution…where do we get that draft link???
For me, I go to see the draft page and copy the link ex: https://phuylai.wordpress.com/?p=198….what’s wrong with it?

4. I just try to open it in other browser! it doesn’t work so it means it can only the owner of blog can see! so our way is wrong heuy!
we have to find new solution heuy !

• If u found out another solution, tell me pong!!