sum

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afif mansib ch
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sum

Unread post by afif mansib ch » Tue Jun 12, 2012 8:28 pm

let s={1,3,5,7}
find\[\sum_{n \in s}n\]
the sol is given in P.t.c. but i'm unable to understand it. :oops: can anyone give a brief sol please?

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*Mahi*
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Re: sum

Unread post by *Mahi* » Tue Jun 12, 2012 10:49 pm

$\sum_{n \in s}n$ means sum of all elements of $s$. Hope this helps.
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SANZEED
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Re: sum

Unread post by SANZEED » Tue Jun 12, 2012 11:30 pm

That means the answer is $16$?
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nayel
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Re: sum

Unread post by nayel » Wed Jun 13, 2012 12:54 am

Yes, the answer is $16$. $\sum_{n\in s}n$ means "sum over $n$ which satisfy $n\in s$". Anything under the summation notation is a condition that the summand(s) need to satisfy. Similarly, $\sum_{x,y\in\mathbb N, x+y=3} xy$ means "sum over all possible $xy$ where $x,y$ satisfy $x,y\in\mathbb N$ and $x+y=3$". What do you think the answer for this sould be?
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SANZEED
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Re: sum

Unread post by SANZEED » Wed Jun 13, 2012 1:17 am

Isn't it $2$?
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nayel
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Re: sum

Unread post by nayel » Wed Jun 13, 2012 1:28 am

No, it is $4$. Because all possible solutions to $x,y\in\mathbb N$ and $x+y=3$ are $x=1,y=2$ and $x=2,y=1$ so all possible $xy$ are $1\cdot 2$ and $2\cdot 1$, and so the sum is $2+2=4$.
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afif mansib ch
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Re: sum

Unread post by afif mansib ch » Thu Jun 14, 2012 12:33 am

actualyy i think i should've explained it.the first problem was to find s.the ans is 64.
the second one was to find the sum of all integers that can be formed from the set.i tried it doing with nt which did work.the ans is 117856.how can i do it with combi?

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afif mansib ch
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Re: sum

Unread post by afif mansib ch » Thu Jun 14, 2012 12:35 am

of course the notation denotes ans is 16.bt the provlem was not to find that.bt it was given in the book.

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SANZEED
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Re: sum

Unread post by SANZEED » Fri Jun 15, 2012 6:59 am

nayel wrote:No, it is $4$. Because all possible solutions to $x,y\in\mathbb N$ and $x+y=3$ are $x=1,y=2$ and $x=2,y=1$ so all possible $xy$ are $1\cdot 2$ and $2\cdot 1$, and so the sum is $2+2=4$.
Nayel vaia, we need to take permutations into account too?
afif mansib ch wrote:of course the notation denotes ans is 16.bt the provlem was not to find that.bt it was given in the book.
And I think you should post the solution given in the book.then we can understand it properly.
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