USING BERNOULLI NUMBERS TO GENERALIZE A LIMIT OF FINITE SUM ARISING FROM VOLUME COMPUTATIONS WITH THE SQUEEZE THEOREM

We developed in this work the computation of the volume of the sphere via the method of exhaustion by inscribed truncated right cones. We show that this computation can be used in calculus courses in several ways; mainly, to motivate and clarify the usage of the squeeze theorem in the computations of sum limits. As a result, we generalized a sum limit using Bernoulli numbers, producing a magnificent example of applied mathematics, and highlighting the importance of exploring when studying mathematics.