How many ways you can express a natural number with sum of only $1$ and $2$. The ordering matter. $3$ can be expressed in 3 ways: $$3=1+1+1=1+2=2+1$$I have found that it can be done by this way.(Nc0)(1/0!)+((N)c1)(1/N)+((N)c2)(1/((N)(N-1)))+...(Nck)(1/N(N-1)*(N-2)...(N-K+1)).where N is the maximum no of 1's to represent N as sum of . so that is N for sure. and k is the quotient you get by dividing n by 2. so i wanna ask that is there a simpler form to represent the sum
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1I do not understand your notations . Could you provide examples to explain them? On the other hand, could you use latex? – Stéphane Jaouen Mar 17 '24 at 11:54
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2Please use MathJax. Here is a tutorial. – Dietrich Burde Mar 17 '24 at 12:05
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i am new to latex – Swastik Sanyal Mar 17 '24 at 12:32
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Please, don't yell. – jjagmath Mar 17 '24 at 12:33
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The sum mentioned by the OP in their work is probably the same in the linked dupe. My answer in the linked dupe and an answer here explicitly address the OP's question. – D S Mar 17 '24 at 12:58
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ok i can see there is the same answer posted.i didn't know that before. i am new to this site. i thought i should ask help on this but didn't know there will this much comments and reply and i will be questioned as if i did duplicity. Whatever i will keep all this in my mind and take care next time. – Swastik Sanyal Mar 17 '24 at 13:04