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Hydrogen (1 H) has three naturally occurring isotopes: 1 H, 2 H, and 3 H. 1 H and 2 H are stable, while 3 H has a half-life of 12.32 (2) years. [3][nb 1] Heavier isotopes also exist; all are synthetic and have a half-life of less than 1 zeptosecond (10 −21 s). [4][5] Of these, 5 H is the least stable, while 7 H is the most.
In mathematics, the harmonic series is the infinite series formed by summing all positive unit fractions: The first terms of the series sum to approximately , where is the natural logarithm and is the Euler–Mascheroni constant. Because the logarithm has arbitrarily large values, the harmonic series does not have a finite limit: it is a ...
The possible screw axes are: 2 1, 3 1, 3 2, 4 1, 4 2, 4 3, 6 1, 6 2, 6 3, 6 4, and 6 5. Wherever there is both a rotation or screw axis n and a mirror or glide plane m along the same crystallographic direction, they are represented as a fraction n m {\textstyle {\frac {n}{m}}} or n/m .
Finally, in late January 2024, he unveiled the album, titled "lonely boy". The release date was set on February 2, and was subsequently released with a track list of 26 songs. 2 weeks later on February 16, a deluxe edition of the album was released. This version added 18 more songs for a total of a 44 song track listing.
The partial sums of the series 1 + 2 + 3 + 4 + 5 + 6 + ⋯ are 1, 3, 6, 10, 15, etc.The nth partial sum is given by a simple formula: = = (+). This equation was known ...
In number theory, the partition function p(n) represents the number of possible partitions of a non-negative integer n. For instance, p(4) = 5 because the integer 4 has the five partitions 1 + 1 + 1 + 1, 1 + 1 + 2, 1 + 3, 2 + 2, and 4. No closed-form expression for the partition function is known, but it has both asymptotic expansions that ...
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