"Shortly after his arrival in Paris in 1672, [ Leibniz ] noticed an interesting fact about the sum of differences of consecutive terms of a of numbers. Given the sequencea_0, a_1, a_2, ..., a_nconsider the sequenced_1, d_2, ..., d_nof differences d_i = a - a_i. Thend_1 + d_2 +... + d_n = (a_1 - a_0) + (a_2 - a_1) + ... (a_n - a_{n-1})= a_n - a_0. Thus the sum of the consecutive differences equals the difference of the first and last terms of the original sequence. ... His result on sums of differences also suggested... the possibility of summing an infinite series of numbers. ... If, in addition, \lim_{n\to \infty} a_n = 0[ -\sum_{n=1}^\infty d_n= a_0 ]"