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5 votes
2 answers
157 views

Sum up to number $N$ using $1,2$ and $3$

So the question asked was finding out the number of ways(combinations), a given number $N$ can be formed using the sum of $1,2$ or $3$. (eg) For $n = 8$, the answer is $10$ The given solution for ...
4 votes
4 answers
2k views

Index change of variable with product

This is probably a dumb question, but oh well here it is: One day a student came to me and asked: Why isn't $$ \sum_{k=0}^{\infty} \frac{1}{2^{2k}}=\sum_{n=0}^{\infty} \frac{1}{2^{n}}$$ using a ...

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