Summing Series: 1/(n!*n) and 1/(n!*n^2) | Math Homework Help

  • Thread starter Thread starter zli034
  • Start date Start date
  • Tags Tags
    Series Sum
zli034
Messages
106
Reaction score
0

Homework Statement


I just trying to sum this series, 1/(n!*n) n from 1 to infinity. also similar 1/(n!*n^2)


Homework Equations



\sum\frac{1}{(n!*n)}
\sum\frac{1}{(n!*n^2)}

The Attempt at a Solution


I know\sum\frac{1}{n!}=e
\sum\frac{1}{n}=ln

My math technique is rusty, can anyone help? thanks in advance. ciao
 
Physics news on Phys.org
The sum of 1/n isn't ln. It diverges. And both of those sums involve nasty non-elementary functions. I only know this because I looked them up. Why do you think you have to evaluate them exactly? A numerical approximation to both converges very rapidly.
 
Thanks. I am doing study on statistics. On some topic I have sum up probabilities of infinite number of events. I have done numberical approximation with excel, and the result is equivalent to a specific event. I was trying to show why.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
View full post »

Similar threads

Show that the limit (1+z/n)^n=e^z holds
Replies
6
Views
2K
Proving convergence and divergence of series
Replies
3
Views
1K
How to show that these sequences are summable?
Replies
1
Views
1K
Integral of x^n using Reimann sums
Replies
4
Views
1K
Doubt regarding the series ##\sum [\sqrt{n+1} - \sqrt{n}\,]##
Replies
17
Views
2K
Prove that this series converges uniformly on R
Replies
4
Views
1K
Frequencies for harmonic oscillator with multiple periodic solutions?
Replies
6
Views
996
Convergence of series log(1-1/n^2)
Replies
2
Views
3K
Finding 2 solutions of this Bessel's function using a power series
Replies
8
Views
2K
What is the Interval of Convergence for the Series ##\sum\frac{n^n}{n!}z^n##?
Replies
3
Views
1K

Hot Threads

Recent Insights

Back
Top