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Determine the value of the following series $\sum^{\infty}_{n=1}(\frac{4}{n^2+4n+3}-9^{-n+2}4^{n+1})$ Solution To determine their value, we must check if the series is a…

What is the difference between $\frac{dy}{dx}$ and $\frac{d}{dx}$ in Calculus? In Calculus, when we write $\frac{dy}{dx}$, it means we are differentiating the function $…

Proving the Madhava-Leibniz series for pi(π)  One of the earliest known approximations of $\pi$ was done by an Indian mathematician Madhava of Sangamagrama during th…

Why does pi have a constant value of 3.14159265359...?  can we define other values for pi?  $\pi$ is a lowercase greek letter used as a mathematical constant pronounced …

Find the second derivative of $y=\sqrt{3x^2-2x+1}$ By indices $y=(3x^2-2x+1)^\frac{1}{2}$ We use chain rule to evaluate $y$.  Formula $\frac{dy}{dx}=\frac{dy}{du}\times…

Why study calculus in real analysis when we can study it in elementary mathematics? Real analysis is an area of analysis that studies concepts such as sequences and thei…