Clear assigned y'[x] from memory
Error entering equation in DSolve
Evaluate $$ 1 + \frac{1}{3}\frac{1}{4}+\frac{1}{5}\frac{1}{4^2}+\frac{1}{7}\frac{1}{4^3}+\dots$$  All i could do was to see that $$\frac{1}{3}=\frac{1}{2.1+1},\frac{1}{5}=\frac{1}{2.2+1},\frac{1}{7}=\frac{1}{2.3+1},\dots$$  SO, we should be able to write   $$ 1 + \frac{1}{3}\frac{1}{4}+\frac{1}{5}\frac{1}{4^2}+\frac{1}{7}\frac{1}{4^3}+\dots=1+\sum_{n=1}^{\infty}\frac{1}{2n+1}.\frac{1}{4^n}$$  This is what i could simplify the given question to...   But, this is doing me no good.. I could not go any further..  I would be thankful if some one can help me to clear this.  I would request users who are trying to help me to just give necessary hints but not post it as answer.  Thank You. Is it a bad practice to catch Throwable? How to determine day of week by passing specific date? Using congruences, show $\frac{1}{5}n^5 + \frac{1}{3}n^3 + \frac{7}{15}n$ is integer for every $n$ What's the application extension? (aka .exe, .app, etc.) I'm new to Ubuntu. What's the application extension for development reasons? I know Windows is mainly .exe and Mac is .dmg or .app. Does Linux have an unique one? What is the best base to use? Swing's KeyListener and multiple keys pressed at the same time Linear regression best polynomial (or better approach to use)? Any ideas on other polynomials I could successfully use for applying regression? My goal is a solution that has fit error strictly based on the noise. Is this possible since it is a bell-like curve? The tails can be long, short or non-existent. Am I looking for the impossible? Please note it has been a while since I have plunged this far into linear regression.   Anyway, my data points do not fit the $ax+bx^2+c$ polynomial well enough. I would like a replacement for this polynomial to apply regression (or different approach). In the following example, each point misses the fit curve by $20\%$ of the $Y$ range on average (of the data points). I looked at splines, but I do not know how to apply the regression since they look piece-wise.   Example $Y$ values (evenly spaced in $X$). It looks kind of like a bell curve. I would be applying 5 to 50 data points to determine the polynomial coefficients. Ultimately, I am interested in the best $X$ location for the peak based on the data points.     X      Y -40    -21142.1111111111 -30    -21330.1111111111 -20    -12036.1111111111 -10      7255.3888888889   0     32474.8888888889  10     32474.8888888889  20      9060.8888888889  30    -11628.1111111111  40    -15129.6111111111 Use masks as part of materials in cycles Intuitive explanation of binomial coefficient formula Non-standard signature of main() compiles successfully Proving the measure of an increasing sequence of measurable sets is the limit of the measures Show that if $A_1\subseteq A_2\subseteq A_3\subseteq\cdots$ is an increasing sequence of measurable sets (so $A_j\subseteq A_{j+1}$ for every positive integer $j$), then we have $$m\left(\bigcup_{j=1}^\infty A_j\right)=\lim_{j\to\infty}m(A_j)$$  Here is my proof: According to the $\sigma$-algebra property, $\bigcup_{j=1}^{\infty}A_j$ is a measurable set, so it makes sense to talk about $m(\bigcup_{j=1}^{\infty}A_j)$. Firstly, I prove that $\lim_{j\to\infty}m(A_j)\leq m(\bigcup_{j=1}^{\infty}A_j)$. This is because for any given positive integer $N$, $A_N\subseteq \bigcup_{j=1}^{\infty}A_i$, according to monotonicity, we have $m(A_N)\leq m(\bigcup_{j=1}^{\infty}A_i)$. Take the limit,we will have $\lim_{j\to\infty}m(A_j)\leq m(\bigcup_{j=1}^{\infty}A_j)$. Secondly, I prove that $m(\bigcup_{j=1}^{\infty}A_j)\leq \lim_{j\to\infty}m(A_j)$. For any given positive integer $N$, $\bigcup_{j=1}^N A_j = A_N$. According to monotonicity,we have $m\left(\bigcup_{j=1}^N A_j\right)=m(A_N)\leq \lim_{j\to\infty}m(A_j)$. Take the limit, we will have $m\left(\bigcup_{j=1}^\infty A_j\right) \leq \lim_{j\to\infty} m(A_j)$. Combine the above two arguments, we will see that $$m\left(\bigcup_{j=1}^\infty A_j\right)=\lim_{j\to\infty} m(A_j)$$$\Box$  The above is my proof, unlike many books, my proof does not use the property of countable additivity. So I doubt my proof is correct. Who can point out where are my mistakes? It is me who am to blame.    It is I who am to blame.      Which one is correct here? I am bewildered about these two sentences. Can inner classes access private variables? class Outer {      class Inner {     public:         Inner() {}         void func() ;     };  private:     static const char* const MYCONST;     int var; };  void Outer::Inner::func() {     var = 1; }  const char* const Outer::MYCONST = "myconst";   This errors out when I compile with class Outer::Inner' has no member named `var' What is special about square numbers here? I am looking to build a camera trap for wildlife viewing, able to capture pictures (or even videos) in decent quality to be able to identify distinct features. I do however need to be able to see the pictures in real time, so the camera would need some sort of wireless connection to a receiving device such as a phone.  I thought of using an FPV setup as used in drone racing, but the quality and range seems to be quite low, and the strengths of an analog signal seem to be latency and fps, which are both not important to me. It would be nice to have some sort of digital signal to be able to do some editing, such as storing pictures. It would also be cool to connect several cameras to one device.  Are there any solutions to this problem? Would a raspberry pi/arduino setup work in some way? Thanks! Could someone please explain the role of the transistor in this circuit? I have a feeling it has to do with the LC circuit but I'm not sure and don't understand completely. The following is an image of the circuit (the transistor is n-type. It is used in lots of sensors to detect and generate ultrasonic waves. Weird thing in references/bibliography page $A \subseteq \mathcal{R}(N)$ and given that (by inductive definition):   $N ∈ S$. If $a \in R$, then $R \setminus \{a\} \in A$.    I need to prove that for each $A \in S$, $N\setminus A$ is finite. How can I prove this formally? Pdf of the square of a standard normal random variable