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2.3 Trigonometric, ... 7.2 Sum of reciprocal of ... allowing the result to be computed in constant time even when the series contains a large number of ...
The harmonic mean of a set of positive integers is the number of numbers times the reciprocal of the sum of their reciprocals. The optic equation requires the sum of the reciprocals of two positive integers a and b to equal the reciprocal of a third positive integer c. All solutions are given by a = mn + m 2, b = mn + n 2, c = mn.
In mathematics, the Euler–Maclaurin formula is a formula for the difference between an integral and a closely related sum.It can be used to approximate integrals by finite sums, or conversely to evaluate finite sums and infinite series using integrals and the machinery of calculus.
For instance, rearranging the terms of the alternating harmonic series so that each positive term of the original series is followed by two negative terms of the original series rather than just one yields [34] + + + = + + + = + + + = (+ + +), which is times the original series, so it would have a sum of half of the natural logarithm of 2. By ...
[1] [2] The cancellation technique, with part of each term cancelling with part of the next term, is known as the method of differences. An early statement of the formula for the sum or partial sums of a telescoping series can be found in a 1644 work by Evangelista Torricelli, De dimensione parabolae. [3]
The current average rate for a 30-year fixed mortgage is 6.97% for purchase and 6.93% for refinance, up 3 basis points from 6.94% for purchase and up 2 basis points from 6.91% for refinance this ...
In Figure 7 are the PDFs for Method 1, and it is seen that the means converge toward the correct g value of 9.8 m/s 2 as the number of measurements increases, and the variance also decreases. From this it is concluded that Method 1 is the preferred approach to processing the pendulum or other data.
Ramanujan summation is a technique invented by the mathematician Srinivasa Ramanujan for assigning a value to divergent infinite series.Although the Ramanujan summation of a divergent series is not a sum in the traditional sense, it has properties that make it mathematically useful in the study of divergent infinite series, for which conventional summation is undefined.