# Tagged Questions

55 views

### Why do both trig functions have the same Macluarin series?

Both the degree version and the radian version of the trig functions have the same Maclaurin series, yet they are different. How is this possible? How can two different functions have the same ...
53 views

### Sum of Harmonic Numbers

Similar to this question , let $H_n$ be the $n^{th}$ harmonic number, $$H_n = \sum_{i=1}^{n} \frac{1}{i}$$ Is there a similar method to calculate the following?: $$\sum_{i=1}^{n}iH_i$$
16 views

### Compound interest problem with increasing deposits

An Investor starts with an initial investment : $A$ He earns a steady profit of 10 percent per year. But every year he adds additional amount which increases by 15 percent every year. At the end of ...
17 views

78 views

### Summation of exponential series [duplicate]

Evaluate the limit: $$\lim_{n \to \infty}e^{-n}\sum_{k = 0}^n \frac{n^k}{k!}$$ It is not as easy as it seems and the answer is definitely not 1. Please help in solving it.
79 views

### Short form of few series

Is there a short form for summation of following series? $$\sum\limits_{n=0}^\infty\sum\limits_{k=0}^n\dfrac{(-1)^kn!\alpha^{2n}((2y-1)^{2k+1}+1)}{2^{2n+1}(2n)!k!(n-k)!(2k+1)}$$ ...
28 views

84 views

### Is there a known evaluation of $\sum_{k=1}^{\infty} \frac{1}{k^k}$? [duplicate]

Is there a known evaluation of $$\sum_{k=1}^{\infty} \frac{1}{k^k}$$ Wolfram Alpha says that it converges to $\approx 1.29129$.
52 views

### How to power series expand determinants?

Say $g$ is a ($d\times d$) matrix which is given as, $g = g_0 + xg_2 + x^2 g_4 .. +x^{d/2 -1}g_{d-2}+ x^{d/2}(g_d + h_d(log (x)))$ where $d$ is an even number and each $g_i$ is a matrix (same ...
### Find the radius of convergence of $\sum_{n=0}^{\infty} (3^n + (-5)^n) x^{7n}$
I have to find the radius of convergence of the series $$\sum_{n=0}^{\infty} (3^n + (-5)^n) x^{7n}$$ I know that I will have something like $|x^7|<\frac{1}{L}$. I tried finding $R$ with ...
### Taylor Series expansion and first four terms of $7x^2 e^{-4x}$
As the series I got $$\sum_{n=0}^\infty (-1)^n(4x)^n/n!$$ which I think is right. However, I am not sure how to get the first four non zero terms.