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Jun 14, 2014 · Fisk's clever argument shows that to guard a gallery with the shape of a simple polygon with n vertices you never need more than n/3 guards (so that's 9/3 = 3 guards in the example in the figure). That's true for any simple polygon with n vertices, no matter how complicated and irregular it looks.
Oct 18, 2018 · A series of the form \(\displaystyle \sum_{n=1}^∞[b_n−b_{n+1}]=[b_1−b_2]+[b_2−b_3]+[b_3−b_4]+⋯+[b_n−b_{n+1}]+⋯\) is a telescoping series. The \( k^{\text{th}}\) partial sum of this series is given by \( S_k=b_1−b_{k+1}\).
Oct 6, 2021 · Using Summation Notation. To find the total amount of money in the college fund and the sum of the amounts deposited, we need to add the amounts deposited each month and the amounts earned monthly. The sum of the terms of a sequence is called a series. Consider, for example, the following series.
This Maths article explores shapes with 3 sides, looking at curved and straight lines.
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Key points. When transforming a shape, either through translation, reflection or rotation, a congruent shape is produced. Enlargements create shapes that are similar. When two shapes are the same...
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Oct 6, 2021 · Formulas are often used to describe the n th term, or general term, of a sequence using the subscripted notation an. A series is the sum of the terms in a sequence. The sum of the first n terms is called the n th partial sum and is denoted Sn. Use sigma notation to denote summations in a compact manner.
