# Tagged Questions

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### Differentiation with respect to the index of the summation notion?

$$\sum_{t=1}^k \binom{N-1}{t-1} \int[1-F(s)]^{N-1}[F(s)]^{t-1}g(s)\,ds$$ $k\in\mathbb Z ^+$ If I want to find out the effects of changing $k$ (comparative statics), what can I do? Differentiation ...
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### Summation of infinite series

If we know the series sum given below converges to a value $C$(constant) $$\sum_{n=0}^{\infty}a_n =C \tag 2$$ Can we generate following in terms of C. values of $a_n$ will tend to zero as n goes to ...
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### Comfirmation of third derivative of symbolic equation including summation

With previous help I was able to find the first derivative of an equation for a work project. Now I'm after the second and third derivative, for use in a program to find the maximum (Which I must do ...
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### Derivative of Log of Summation of exponential function (base e)

A financial formula that I am implementing requires that I find the first derivative of a function to find a local maxima, from scratch. Can someone please help me with finding the first derivative of ...
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### Calculating derivation of logarithm of summation of products

I am trying to grasp the idea discussed in this paper. In the second section of this paper it calculates the derivative of (1) which results in equation (2). I cannot figure out how the derivative of ...
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### Make derivations over sums

I have this kind of sums $$\left(\sum_{i_1=0}^{4}\sum_{i_2=0}^{4}\log(f(X,i_1,i_2))\right)'\$$ And we want to derive in respect to $${x_i}$$, which is an element of the vector X. How I should do ...
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### How do I calculate the sum of $\sum_{k=1}^{\infty}\frac{(2-x)^k}{2^k\cdot k}$ in every x in (0, 4)?

Well I've been trying to search for the appropriate derivative but I couldn't find it Thanks
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### Help manipulating a sum

Let $S(x,t)=e^{2xt-t^2}=\sum^\infty_{n=0}\frac{H_n(x)}{n!}t^n$ If we now differentiate each term with respect to $x$ we find: \begin{align*} \frac{\partial S}{\partial ...
I am trying to confirm a stated result on my lecture slide. Question: Given that $A:= \sum_i^n \frac{a_i}{(1+b)^{t_i}}$, where $a_i,b \in \mathbb{R}_+$ and $t_i \in \{t_1,...,t_n\}$ where $0 < ... 1answer 201 views ### Computing a finite binomial sum I want to compute $$S(n,m,a)=\sum_{k=0}^{n}k^{m}\cdot\binom{n}{k}\cdot a^k.$$ With$n,m\in\mathbb N$,$a\neq0$and$S(n,0,a)=(a+1)^n\$. What I have found already: I don't see any other options then ...
I am trying to understand a step in the math given a scientific paper. They differentiate an objective function of the form: $$snr = \frac{\sum_{i=1}^n x_it_i}{\sum_{i=1}^n x_id_i}$$ To maximize ...