sum
- afif mansib ch
- Posts:85
- Joined:Fri Aug 05, 2011 8:16 pm
- Location:dhaka cantonment
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. can anyone give a brief sol please?
find\[\sum_{n \in s}n\]
the sol is given in P.t.c. but i'm unable to understand it. can anyone give a brief sol please?
Re: sum
$\sum_{n \in s}n$ means sum of all elements of $s$. Hope this helps.
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Nur Muhammad Shafiullah | Mahi
Re: sum
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?
"Everything should be made as simple as possible, but not simpler." - Albert Einstein
Re: sum
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 $2+2=4$.
"Everything should be made as simple as possible, but not simpler." - Albert Einstein
- afif mansib ch
- Posts:85
- Joined:Fri Aug 05, 2011 8:16 pm
- Location:dhaka cantonment
Re: sum
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?
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?
- afif mansib ch
- Posts:85
- Joined:Fri Aug 05, 2011 8:16 pm
- Location:dhaka cantonment
Re: sum
of course the notation denotes ans is 16.bt the provlem was not to find that.bt it was given in the book.
Re: sum
Nayel vaia, we need to take permutations into account too?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 $2+2=4$.
And I think you should post the solution given in the book.then we can understand it properly.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.
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