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Dec 4, 1999 · Gene Rayburn, who became a mainstay on television from the 1960's to the 80's as the amiable host of ''The Match Game,'' died on Monday at his home in Beverly, Mass. He was 81. The cause was...
If we start indexing at $n = 1$, we get $$a_n = 2^{\lceil \log_2 n\rceil}$$where $\lceil - \rceil$ is the ceiling function.
Match Game. Rayburn on the set of Match Game 76. From 1962 to 1969, Rayburn hosted The Match Game. In the original version, which aired from New York on NBC, Rayburn read questions to two panels, each consisting of a celebrity and two audience members.
If you apply the 'digit-sum' operator to the added number repeatedly, you can make the sequence $1, 2, 4, 8, 7, 5, \dots$. For instance, from $1991$ to $2021$ , you add $20$ (the digit sum of $20$ itself is $2$ ).
The general form of these things is: a, ar, ar 2 ,ar 3 , ar r,.... For this example a= 1 , r= 2. Note the cases with r=1 are not interesting. When r>1 the sequence tends to infinity When -1<r<1 the sequence will tend to 0.
$$" x = 1 + 2 + 4 + 8 + 16 + ... "$$ They are already suspicious - it is peculiar giving $\infty$ a name like $x$, and so I can tell they already know that something strange is afoot. " Note that $2x = 2 + 4 + 8 + ... = x - 1$."
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Algebra. Identify the Sequence 2 , 4 , 8 , 16. 2 2 , 4 4 , 8 8 , 16 16. This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by 2 2 gives the next term. In other words, an = a1rn−1 a n = a 1 r n - 1. Geometric Sequence: r = 2 r = 2.
