If N = 1111112, find the sum of digits in the expansion of N.


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Answer:

36

Step by Step Explanation:
  1. We know that the square of 11 is equal to 110 + 11, which is 121. The sum of digits of 121 is equal to 4.
  2. The square of 111 will be equal to 111 + 1110 + 11100 = 12321, whose sum of digits is equal to 9.
  3. Similarly, the sum of 1111 will be equal to 1111 + 11110 + 111100 + 1111000 = 1234321, whose sum of digits is equal to 16.
  4. The sum of digits of squares of such numbers is following a pattern, which is the square of all natural numbers.
  5. If we follow the same analogy as discussed above, the sum of digits of 1111112 will be equal to 36.

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