Almost Alternating Sums
Kevin O’Bryant, Bruce Reznick, Monika Serbinowska · American Mathematical Monthly · 2006
as N -> oo is not transparent (here [x signifies the greatest integer not larger than x). The random walk J2n= wm where the wn are independent random variables taking the values 1 and ? 1 with equal probability, is known to have absolute value typically around c\f? for an appropriate constant c and large N [23]. Knowing this and know ing also that for irrational a the sequence a is random-ish modulo 2, a natural guess is that |Sw(a)| is also around \//V. Contrary to this expectation, for almost all real numbers a