Question

Find the sum of the digits of the number 6 + 66 + 666 + 6666 + ... + 666...66, where the last number contains 100 digits.

A. 450
B. 505
C. 550
D. 605

Answer 1

The sum of the digits for the given series is 600.

Step-by-step explanation:

To find the sum of the digits of the given series, we can observe that each term represents a number with a pattern:

• The first term, 6, has a sum of digits 6.
• The second term, 66, has a sum of digits 6 + 6 = 12.
• The third term, 666, has a sum of digits 6 + 6 + 6 = 18.
• And so on, until the 100th term, which is a number with 100 digits, all equal to 6.

We can see that the sum of digits for each term is equal to the number of digits multiplied by 6. Therefore, the sum of the digits for the 100th term is 100 * 6 = 600. However, since all digits are equal to 6, the sum of digits for the 100th term is 100 * 6 = 600.