Question

1. Calculate each of the following:
=
13 +53 +33 =
163 +503 + 333
1663 +5003 + 3333
16663 + 50003 + 33333
??
??
??
??
=
What do you see? Can you state and prove a generalization of your observations?​

Answer 1

Answer:

13 +53 +33 =

163 +503 + 333

1663 +5003 + 3333

16663 + 50003 + 33333: 111066

Answer 2

13 + 53 + 33 = 99

163 + 503 + 333 = 999

1663 + 5003 + 3333 = 9999

16663 + 50003 + 33333 = 99999

• From the calculations above, we can observe that the sum is 99, 999, 9999, 99999.....
• The sum of numbers formed by repeating a digit "n" by 1 each time (such as 3, 33, 333, etc.) in increasing order, results in a number with all its digits being "9" and the number of digits of the resulting number is the number of digits in numbers we are adding in sum.
• This is because, we are adding numbers whose digits are all 3s or 6s, so we can notice that the sum of each column is always 9 (when adding three 3s or one 6 and one 3).

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