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anemone
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Show that $\displaystyle \sum_{k=0}^{2013} \dfrac{4026!}{(k!(2013-k)!)^2}$ is the square of an integer.
The square of an integer is the result of multiplying the integer by itself. For example, the square of 5 is 25 (5 x 5 = 25).
The square of an integer can be shown by using an exponent of 2. For example, 5 squared can be written as 52, which is equivalent to 25.
An integer is a whole number, whereas its square is the result of multiplying the integer by itself. For example, the integer 5 is not the same as its square, 25.
Yes, negative numbers can have a square. When a negative number is squared, the result is a positive number. For example, (-3)2 = 9.
The square of an integer is useful in many mathematical equations and concepts such as calculating the area of a square, finding the distance between two points on a graph, and solving quadratic equations. It is also used in various scientific fields, such as physics and engineering.