Wobster109: the numbers 1 through 708, inclusive, are printed on a piece of paper. how many digits are printed on the paper?

Given: Numbers 1 to 708, inclusive

Find:

Total digits printed on the paper = ?

Solution:

1 to 9 = 9 - 1 + 1 = 8 + 1 = 9 * 1 digit = 9
10 to 99 = 99 - 10 + 1 = 89 + 1 = 90 * 2 digits = 180

100 to 708 = 708 - 100 + 1 = 608

608 + 1 = 609 * 3 digits = 1827 

total = 9 + 180 + 1827 = 2016 

Therefore, the total number of digits that are printed on the paper is 2016 digits.

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

answer: 0.1,0.85

step-by-step explanation: