441. In the table of reciprocal values of natural numbers (school tables of Schlemilch, table VI), the difference between the reciprocal values of two consecutive numbers decreases and very quickly, as we move towards the reciprocal values of increasingly larger numbers. Verify this directly. Explain why this should be the case.
441. $\frac{1}{n}-\frac{1}{n+1}=\frac{1}{n(n+1)}<\frac{1}{n^{2}} ;$ for example, when $n=1000$ the corresponding difference is less than 0.000001.