EndCaking&Agglomeration

\begin{align*} s_n(1-x)\amp =k(1-x^{n+1})\\ s_n\amp =k{1-x^{n+1}\over 1-x}\text{.} \end{align*} If \(|x|\... When \(c\) is non-zero, the converse of the first p...

\begin{align*} \left| \begin{matrix} x \amp y \amp z\\ v_1 \amp v_2 \amp v_3\\ w_1 \amp w_2 \amp w_3 \end{matrix}\right| \amp =x\left| \begin{matrix} v_2 \amp v...

\begin{equation*} \begin{array}{l|lllllll} n \amp 1 \amp 2 \amp 3 \amp 4 \amp 5 \amp 6 \amp \dots \\ \hline s_n \amp 1 \amp 0.875 \amp 0.912...\amp 0.896... \am...

\begin{equation*} \begin{split} \int (2y - \sec^2 y) \,dy \amp = 2\int y\,dy - \int \sec^2 y\,dy\\ \amp = 2\left(\frac{1}{2}y^2+C_1\right) - \left(\tan y + C_2\...

\begin{equation*} \begin{split} f'(a)\amp=\lim_{x\to a}\frac{f(x)-f(a)}{x-a}\\ \amp=\lim_{x\to a}\frac{x^n-... r(x)}{h}}\\ \\ ~\amp =\amp \ds{\lim_{h\to 0}...

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\,dy\amp = \int \left(1-4y^2\right)^{-1/2}(2y~dy)\\ \amp = \int u^{-1/2}\left(-\frac{1}{4}du\right)\\ \amp =\left(\frac{-1}{4}\right)\frac{u^{1/2}}{1/2}+C\\ \am...