1. Find the sum of all multiples of x in the closed interval [α . . β], when x > 0. 2. How many of the numbers  have leading digit 1 in decimal notation? 3. Evaluate the sums 4. Show that the nth...

1. Find the sum of all multiples of x in the closed interval [α . . β], when x > 0.

2. How many of the numbers
 have leading digit 1 in decimal notation?

3. Evaluate the sums

4. Show that the nth element of the sequence

1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, . . .

is
 (The sequence contains exactly m occurrences of m.)