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In mathematics, the infinite series 1 / 2 + 1 / 4 + 1 / 8 + 1 / 16 + ··· is an elementary example of a geometric series that converges absolutely. The sum of the series is 1. In summation notation, this may be expressed as
where f (2k−1) is the (2k − 1)th derivative of f and B 2k is the (2k)th Bernoulli number: B 2 = 1 / 6 , B 4 = − + 1 / 30 , and so on. Setting f ( x ) = x , the first derivative of f is 1, and every other term vanishes, so [ 15 ]
1 ♠ – 2 ♣ 2 ♦ – 3 ♣ Forcing, unless the partnership has agreed that this is an exception to the "2/1 rule." 1 ♦ – 2 ♣ Forcing for one round only (as in Standard American), except in the variant of 2/1 where this sequence is game forcing as well. 1 ♣ – 2 ♣ Forcing for one round; 10 points or more with at least four clubs ...
For some other divergent geometric series, including Grandi's series with ratio −1, and the series 1 + 2 + 4 + 8 + ⋯ with ratio 2, one can use the general solution for the sum of a geometric series with base 1 and ratio , obtaining , but this summation method fails for 1 + 1 + 1 + 1 + ⋯, producing a division by zero.
Angelina Jolie on Dec. 2, 2024 Jolie is considered an awards season frontrunner for her performance in Maria ; accordingly, she received the Gotham Awards' Performer Tribute for the movie on Dec. 2.
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