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Results tagged with differential-calculus
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user 169474
10
votes
Solving a limit about sum of series
The function $x \mapsto t^{x^2}$ decreases on $\mathbb{R}_+$, so for every $n \in \mathbb{N}$,
$$t^{(n+1)^2} \le \int_n^{n+1}t^{x^2}dx \le t^{n^2}$$
By summation over $n$,
$$\sum_{n=1}^{\infty}t^{n^2} …
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