# Sum of Digits

Find the sum of digits of $$10^{2014} - 2014$$.

Note by Dev Sharma
2 years, 9 months ago

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There'll be 2010 9's followed by 7, 9 , 8, 6. So the sum of digits becomes 18120

- 2 years, 9 months ago

See there is a pattern $10^4 - 2014 = 7986$ $10^5 - 2014 = 97986$ $10^6 - 2014 = 997986$ $10^7 - 2014 = 9997986$ Like this. $10^n - 2014 =\underbrace{(9999\ldots)}_{(n-4)\quad times}7986$ Thus, $10^{2014} - 2014 = \underbrace{(9999\ldots)}_{(2010)\quad times}7986$ Thus sum of digits = $2010 * 9 + 7 + 9 + 8 + 6 = 18120$

- 2 years, 8 months ago

nice observation

- 2 years, 8 months ago

thank you

- 2 years, 8 months ago