B5

Part of 1983 Putnam

Problems(1)

limit integral with distance to nearest integer

Source: Putnam 1983 B5

\lVert u\rVert

denote the distance from the real number

u

to the nearest integer. For positive integers

n

a_n=\frac1n\int^n_1\left\lVert\frac nx\right\rVert dx.

\lim_{n\to\infty}a_n

calculusintegrationlimits