# Questions tagged [convergence]

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### Convergence of $\left\{n!\sum_{k=1}^{n!}\frac{1}{k^{\frac{3}{2}}}\right\}$ as $n\to \infty$ using Mathematica or otherwise

Using Mathematica or otherwise, I need to find the convergence or divergence of$$\lim_{n\to\infty}\left\{n!\sum_{k=1}^{n!}\frac{1}{k^{\frac{3}{2}}}\right\}$$ where $\{x\}$ denotes the fractional part ...
• 155
50 views

### Find radius of convergence for two series product [closed]

I have a equation like this: (u + v + w + 2 u w + 2 v w + 2u v + 3u v w)/[1 - (v w + uv + uw + 2 u v w)] ...
• 21
1 vote
46 views

### Find roots for complicated expression involving HarmonicNumber

I have a equation like this: (u + v + w + 2 u w + 2 v w + 2u v + 3u v w)/[1 - (v w + uv + uw + 2 u v w)] ...
• 125
128 views

194 views

### How to judge whether the series is absolutely convergent?

I need to judge whether the series $\sum_{n=1}^{\infty}(-1)^{n}\left(1-\cos \frac{\alpha}{n}\right)$ (α>0) is absolutely convergent. ...
128 views

### Why is the function SumConvergence not valid for simple power series

I want to find the convergence interval of function $\sum_{n=1}^{\infty} \frac{1}{3^{n}+(-2)^{n}} \frac{x^{n}}{n}$. ...
2k views

### How to get the convergence radius of the result of Series? [duplicate]

The Taylor expansion of function is very useful, but the convergence radius of power series results after Taylor expansion is also important. But the result of ...
269 views

### How to verify whether the abnormal integral is convergent or divergent?

How to verify the convergence and divergence of the abnormal integrals $\int_{0}^{1} \frac{\sqrt[m]{\ln ^{2}(1-x)}}{\sqrt[n]{x}} d x$: ...
381 views

### Improving mesh and NDSolve solution convergence

I have developed the code below to solve two PDEs; first mu[x,y] is solved for, then the results of mu are used to solve for phi[x,y]. The code works and converges on a solution as is, however, I ...
• 353
1 vote
64 views

### Speeding up simultaneous numerical integration where some integrals vanish

I would like to carry out a number of numerical integrals in the form of a table: ...
• 1,043
93 views

### Plotting a complex integral function [duplicate]

Can anybody help me to plot the T1 and T2, please? The problem is that the integral part becomes so huge or indeterminate at ...
301 views

### Code that produces plot in V5 doesn't work in later versions

I have problem in plotting Integral function. I can compute/plot the graph of this integration below in Mathematica 5.0, but it is not possible to plot it in higher Mathematica versions. My code is: <...
436 views

### Why doesn't Mathematica provide an answer while Wolfram|Alpha does, concerning a series convergence?

Among other series I've been working on, I was asked to find whether $$\sum_n 1-\cos(\frac{\pi}{n})$$ converged, and Mathematica's output to ...
• 121
62 views

### Nintegrate providing results much smaller than what is expected

This is the first time I am posting something here. So, apologies if I make any mistake. I am dealing with a numerical integration in Mathematica-11.0 that has a Bessel function in it. In order to ...
843 views

### Bug in Integrate?

In v. 11.1.0.0 Mathematica for Linux Integrate[Sin[Cosh[t]], {t, 0, Infinity}] returns Integrate::idiv: Integral of Sin[Cosh[t]] does not converge on {0,[...
• 293
377 views

### Wolfram Language 12 says this absolutely convergent series does not converge. Is there any similar example?

I am reading "Lectures on complex function theory" by Takaaki Nomura. In this book, there is the following example: $\sum_{n=1}^{\infty} \sin(\pi(2+\sqrt{3})^n)$ converges absolutely. But ...
• 463
594 views

### Strange result for sum $\sum _{k=1}^{\infty } \frac{\sin (k (k-1))}{k}$

In this sum over $k$ Sum[Sin[k (k - 1)]/k, {k, 1, ∞}] the result still containes the summation index $k$. ...
• 13.1k