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Let a, b, c be three vectors. Consider the following expressions, these are called scalar triple product of vectors a, b, c. $$(\vec{a} \times \vec{b}) \cdot \vec{c}$$ or $$[\vec{a}\ \vec{b}\ \vec{c}]$$ The above expression is also called Mixed product or Box product. Using permutation of three vectors in six different ways we get total twelve … Read more

It is a series where each term is a multiplication of a term in AP and a GP. The series $$a+(a+d) r+(a+2 d) r^2+\ldots+(a+(n-1) d) r^{n-1}$$ is known as the arithmetico-geometric series. Let’s denote the above sum by $$\begin{aligned}& S_n=a+(a+d) r+(a+2 d) r^2+\ldots+(a+(n-1) d) r^{n-1}\end{aligned}$$ What is an example of an AGP series? $$1+3 \mathrm{x}+5 … Read more