Euler's Solution

Euler's solution to the Basel problem demonstrates that the sum of the reciprocals of the squares of natural numbers (1/1² + 1/2² + 1/3² + ...) equals \(\pi^2/6\). He achieved this by relating the infinite sum to the properties of the sine function through its infinite product expansion. Essentially, Euler analyzed how the zeros of sine relate to its expansion and then linked this to the sum of the reciprocals of squares. This innovative approach bridged infinite series and the geometry of circles, revealing a deep connection between number theory and mathematical constants.