সহজ থেকেও সহজতর

For students of class 6-8 (age 12 to 14)
sakibtanvir
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সহজ থেকেও সহজতর

Unread post by sakibtanvir » Fri Aug 31, 2012 4:34 pm

প্রমাণ কর, $\frac{1}{n}+\frac{1}{n+1}+\frac{1}{n+3}$ একটি পৌনঃপুনিক(Repeated decimal) সংখ্যা যেখানে $n \in\mathbb N$.
An amount of certain opposition is a great help to a man.Kites rise against,not with,the wind.

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SANZEED
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Re: সহজ থেকেও সহজতর

Unread post by SANZEED » Sun Sep 02, 2012 11:09 pm

Sorry but for $n=1$,$\frac{1}{1}+\frac{1}{1+1}+\frac{1}{1+3}=1.75$. However it is true for $n\geq 2$ I think. Use the fact that $\frac{m}{n}$ is in repeated decimal when $n$ has a prime factor other than $2$ and $5$.
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sakibtanvir
Posts:188
Joined:Mon Jan 09, 2012 6:52 pm
Location:24.4333°N 90.7833°E

Re: সহজ থেকেও সহজতর

Unread post by sakibtanvir » Mon Sep 03, 2012 3:23 pm

Sorry,forgot to give the condition :oops: :oops: .
The fact killed the solution actually :)
An amount of certain opposition is a great help to a man.Kites rise against,not with,the wind.

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