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Zazzle is an American online marketplace that allows designers and customers to create their own products with independent manufacturers (clothing, posters, etc.), as well as use images from participating companies.
The series 1 4 + 1 16 + 1 64 + 1 256 + ⋯ lends itself to some particularly simple visual demonstrations because a square and a triangle both divide into four similar pieces, each of which contains 1 4 the area of the original.
This is a list of articles about prime numbers. A prime number (or prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. By Euclid's theorem, there are an infinite number of prime numbers. Subsets of the prime numbers may be generated with various formulas for primes. The first 1000 primes are listed below, followed by lists of notable types of prime ...
^ Ten-codes require transmission of three prefix characters "10-" and two numbers, so five characters, on top of which digits and punctuation are all long sequences in Morse (5–6 dits or dahs).
The infinite sequence of triangular numbers diverges to +∞, so by definition, the infinite series 1 + 2 + 3 + 4 + ⋯ also diverges to +∞. The divergence is a simple consequence of the form of the series: the terms do not approach zero, so the series diverges by the term test .
Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The n th triangular number is the number of dots in the triangular arrangement with n dots on each side, and is equal to the sum of the n natural numbers from 1 to n.
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