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Find the sum of digits of \(10^{2014} - 2014\).

Note by Dev Sharma 1 year, 7 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 – Vishnu C · 1 year, 7 months ago

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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 = \[2010 * 9 + 7 + 9 + 8 + 6 = 18120 \] – Svatejas Shivakumar · 1 year, 6 months ago

@Svatejas Shivakumar – nice observation – Dev Sharma · 1 year, 6 months ago

@Dev Sharma – thank you – Svatejas Shivakumar · 1 year, 6 months ago

@Nihar Mahajan @Niranjan Khanderia @Swapnil Das @Akshat Sharda @naitik sanghavi – Dev Sharma · 1 year, 7 months ago

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TopNewestThere'll be 2010 9's followed by 7, 9 , 8, 6. So the sum of digits becomes 18120 – Vishnu C · 1 year, 7 months ago

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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 = \[2010 * 9 + 7 + 9 + 8 + 6 = 18120 \] – Svatejas Shivakumar · 1 year, 6 months ago

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– Dev Sharma · 1 year, 6 months ago

nice observationLog in to reply

– Svatejas Shivakumar · 1 year, 6 months ago

thank youLog in to reply

@Nihar Mahajan @Niranjan Khanderia @Swapnil Das @Akshat Sharda @naitik sanghavi – Dev Sharma · 1 year, 7 months ago

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