31. However, none of the original ancient sources has Zeno discussing the sum of any infinite series . 32. In mathematics, the infinite series is an elementary example of a geometric series that converges absolutely. 33. These questions arise in the study of limit and the infinite series , which resolve the paradoxes. 34. Euler needed it to compute slowly converging infinite series while Maclaurin used it to calculate integrals. 35. The Cauchy product of these two infinite series is defined by a discrete convolution as follows: 36. But Madhava went further and linked the idea of an infinite series with geometry and trigonometry. 37. The Cauchy product of two infinite series is defined even when both of them are divergent. 38. The sum of the sinh and cosh series is the infinite series expression of the exponential function. 39. In general, different rearrangements of an infinite series may yield different sums, unless certain conditions are imposed. 40. Decimal fractions with infinitely many digits to the right of the decimal separator represent an infinite series .
