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le: ∑(n=1 to ∞) 1/n^2 = π^2/6 Have you ever heard of the famous mathematical formula: ∑(n=1 to ∞) 1/n^2 = π^2/6? It’s known as the Basel problem, named after the Swiss city where it was first introduced by the mathematician Leonhard Euler in the 18th century. The formula looks quite intimidating at first glance, but it is actually a beautiful expression of the deep connections between geometry and number theory. To understand it, let’s break it down. The symbol ∑ represents a series, or the sum of a sequence of numbers. In this case, we are adding up the terms 1/n^2 for all positive integer values of n, starting from 1 and going up to infinity. So the expression ∑(n=1 to ∞) 1/n^2 represents the sum of the infinite series 1 + 1/2^2 + 1/3^2 + 1/4^2 + … But what is the value of this sum? It turns out to be pi squared over 6, or approximately 1.64493406685. This might seem like a completely arbitrary result, but in fact it reveals a surprising connection between two seemingly unrelated areas of mathematics: trigonometry and number theory. If you take the series of sine(x)/x for x ranging from 1 to infinity, and you integrate this series from 0 to infinity, you get the same result as the sum of 1/n^2. This relationship between the sum of squares and the trigonometric functions is a deep insight into the nature of mathematics. The Basel problem is just one example of the beauty and richness of mathematical exploration. It reminds us that even the simplest-seeming questions can lead to profound and unexpected insights, and that the wonder of mathematics lies 「学习更多 属相婚配知识请关注 :好姻缘网,Www.HaoYInyUan.cC］）in the connections and patterns that underlie all of science.