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If n = 10^{2020} + 10^{2019} + 10^{2018} + 10^{2017} + ... + 10^2 + 10^1, what is the sum of digits of the integer n? 

 Jul 9, 2022
 #1
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Looks hard but is actually easy!

The number, 10^n is just 1000... with n zeroes. Now suppose we have the 1 on the digits place next to it when we add 10^{n-1}. What do you get?

So by this observation, we can see that your whole expression is equal to:
11111... with 2020 1's.

 

Therefore, the sum of the digits of that epxession is 2020 x 1 = 2020. 

 Jul 9, 2022
 #2
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Now solve this https://web2.0calc.com/questions/need-help-with-this_18

Guest Jul 9, 2022

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