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Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011.
In mathematics, the nth-term test for divergence [1] is a simple test for the divergence of an infinite series: If lim n → ∞ a n ≠ 0 {\displaystyle \lim _{n\to \infty }a_{n}\neq 0} or if the limit does not exist, then ∑ n = 1 ∞ a n {\displaystyle \sum _{n=1}^{\infty }a_{n}} diverges.
Starting with iOS 17, it was reported that Wolfram for Siri no longer answers mathematical equations, instead defaulting to web search queries with no notable explanation. [ 20 ] [ 21 ] WolframAlpha data types [ clarification needed ] , sets of curated information and formulas that assist in creating, categorization, and filling of spreadsheet ...
It concerns sequences of integers in which each term is obtained from the previous term as follows: if a term is even, the next term is one half of it. If a term is odd, the next term is 3 times the previous term plus 1. The conjecture is that these sequences always reach 1, no matter which positive integer is chosen to start the sequence.
The same central binomial coefficient () is also the number of words of length 2n made up of A and B within which, as one reads from left to right, there are never more B 's than A 's at any point. For example, when n = 2 {\displaystyle n=2} , there are six words of length 4 in which each prefix has at least as many copies of A as of B : AAAA ...
Every non-zero number x, real or complex, has n different complex number nth roots. (In the case x is real, this count includes any real nth roots.) The only complex root of 0 is 0. The nth roots of almost all numbers (all integers except the nth powers, and all rationals except the quotients of two nth powers) are irrational. For example,
Proof without words of the arithmetic progression formulas using a rotated copy of the blocks. An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence. The constant difference is called common difference of that ...
def f (x): return x ** 2-2 # f(x) = x^2 - 2 def f_prime (x): return 2 * x # f'(x) = 2x def newtons_method (x0, f, f_prime, tolerance, epsilon, max_iterations): """Newton's method Args: x0: The initial guess f: The function whose root we are trying to find f_prime: The derivative of the function tolerance: Stop when iterations change by less ...