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Aug 30, 2011 · Sound Horizon's performance of the song Yuigon, which has only been performed live, from the TTE III Live day 1. The vocals are performed by Revo. Please support Sound Horizon by buying...
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Since $x^{n-1} + x^{n-2} y + \dots + x y^{n-2} + y^{n-1}$ is a geometric series with $n$ terms and a common factor of $y/x$, it equals $$ \frac{x^{n-1}\left(1-\left(\frac{y}{x}\right)^n\right)}{1-\frac{y}{x}}=\frac{x^{n}\left(1-\left(\frac{y}{x}\right)^n\right)}{x-y}=\frac{x^n-y^n}{x-y} \, ; $$ multiplying through by $(x-y)$ gives the desired ...
- You have everything right except the last line. Maybe it is easier to do in this order: $$(x−y)\left(x^{n−1}+x^{n−2}y+\cdots+xy^{n−2}+y^{n−1}\right...
- I think it would be easier for you to recall $$\left(1+x+x^2+\cdots+x^{n-1}\right)(x-1) = x^n-1$$ and put $x=\dfrac{b}{a}$ $$\eqalign{ & \left( {...
- Here is the inductive step, presented more conceptually $$\rm\frac{x^{n+1}-y^{n+1}}{x-y}\: =\ x^n\: +\ y\ \frac{x^n-y^n}{x-y}$$ So, intuitively, pr...
- Your method is sound, you just made a sort of arithmetic mistake. When cancelling or otherwise combining two sequences, try explicitly lining thing...
- The $x^2 y^{n-2}$ term from $x \cdot x y^{n-2}$ is cancelled by the term from $(-y) \cdot x^2 y^{n-3}$. Similarly, the $(-y) \cdot x^{n-2} y$ is...
- Since powers of x and y is always greater than or equal to zero, You can prove it by mathematical induction.
- Sorry but I don't speak English well but I will try to write as correctly as possible. Your demonstration is correct, but your idea of cancellation...
- Since $x^{n-1} + x^{n-2} y + \dots + x y^{n-2} + y^{n-1}$ is a geometric series with $n$ terms and a common factor of $y/x$ , it equals $$ \frac{x...
- Using Induction Hypothesis Let n =k Then , x^k -y^k = (x-y)(x^(k-1) +x^(k-2) y ....+y^k-1) Let n= (k-1) Then by Induction Hypothesis, (x-y){x(x^(k-...
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Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.
Aug 19, 2018 · As an exercise in learning Matplotlib and improving my math/coding I decided to try and plot a trigonometric function (x squared plus y squared equals one). Trigonometric functions are also called "circular" functions but I am only producing half the circle.
Solve for x Calculator. Step 1: Enter the Equation you want to solve into the editor. The equation calculator allows you to take a simple or complex equation and solve by best method possible. Step 2: Click the blue arrow to submit and see the result!
First-Order Linear Equations. Solve first-order linear differential equations: y' (t) - 2y (t) = 3 e^ (2t) x y' (x) - 4 y (x) = x^6 exp (x), y (1) = 0. See the steps for using Laplace transforms to solve an ordinary differential equation (ODE): solve y' (t) - 3y (t) = delta (t - 2), where y (0) = 0.
