Problem: Find the sum of the digits of all the numerals in the sequence 1,2,3,4,⋯,10000.
Answer Choices:
A. 180001
B. 154756
C. 45001
D. 154755
E. 270001
Solution:
Omit 10,000 for the moment. In the sequence 0000,0001,0002,0003,⋯,9999 each digit appears the same number of times. There are (10,000)(4) digits in all, each digit appearing 4,000 times. The sum of the digits is 4,000(0+1+2+⋯+9)= 4,000(45)=180,000. Now add the 1 in 10,000 to get 180,001 .