If you disregard the very simplest cases, there is in all of mathematics not a single infinite series whose sum has been rigorously determined. In other words,the most important parts of mathematics stand without a foundation.
Niels H. Abel (1802 - 1829)
Source: G. F. Simmons, Calculus Gems, New York: Mcgraw Hill, Inc., 1992, p. 188.
Contributed by: Zaady