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Results tagged with sequences-and-series
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user 4213
for questions about sequences and series, e.g. convergence, closed form expressions, etc. Note that there is a different tag for spectral sequences, and also note that MathOverflow is not for homework. Please consider consulting the online encyclopedia for integer sequences, if you are trying to identify a given sequence that you have found in your research.
8
votes
Accepted
mertens-function in the light of divergent summation - what summation method were best adapted
Well,
$$\sum_{n=1}^\infty\frac{\mu(n)}{n^s}=\frac1{\zeta(s)}$$
for $s>1$, so setting $s=0$ should give
$$\sum_{n=1}^\infty\mu(n)=\frac1{\zeta(0)}=-2$$
as $\zeta(0)=-1/2$. :-)
I should add that this i …
- 20.8k
15
votes
Accepted
fibonacci series mod a number
This is really just an expansion of Gerhard's comment. One has the matrix formula
$$\begin{pmatrix}
1&1\\\
1&0
\end{pmatrix}^n=
\begin{pmatrix}
F_{n+1}&F_n\\\
F_n&F_{n-1}
\end{pmatrix}
$$
so the probl …
- 20.8k