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Results tagged with limits-and-convergence
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user 13832
Convergence of series, sequences and functions and different modes of convergence.
1
vote
Accepted
Question about exponential-type limit
Counterexample: Define $N(m)$ by
$$N(m):=\begin{cases}
\lfloor n!/2\rfloor &\text{if } m=(n+2)!-1\\\\
\lceil n!/2\rceil &\text{if } m=(n+2)!\\\\
0 &\text{otherwise}\\\\
\end{cases}$$
and note that $\s …
- 881
6
votes
Accepted
asymptotic behaviour of a sum
Let $T_N(x)$ denote the largest term of the sum. Note that
$$\frac{\log T_N(x)}{N}\leq \frac{\log (Z_N(x))}{N}\leq \frac{\log ((N/2)T_N(x))}{N}=\frac{\log T_N(x)}{N}+\frac{\log(N/2)}{N}$$
and that th …
- 881