Difference between revisions of "2021 JMPSC Accuracy Problems/Problem 15"
(Created page with "==Problem== For all positive integers <math>n,</math> define the function <math>f(n)</math> to output <math>4\underbrace{777 \cdots 7}_{n\ \text{sevens}}5.</math> For example,...") |
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− | + | Notice that <math>\frac{f(1)}{25} = 19</math>, <math>\frac{f(2)}{25} = 191</math>, <math>\frac{f(3)}{25} = 1911</math>, and <math>\frac{f(n)}{25}</math> ends in <math>111</math> for all <math>n \ge 4</math>. So, the last 3 digits of <math>\frac{f(1)+f(2)+ \cdots + f(100)}{25}</math> are the last <math>3</math> digits of <math>19 + 191 + 911 + 111 \cdot 97</math>, which are <math>\boxed{888}</math>. | |
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+ | ~Mathdreams |
Revision as of 11:34, 11 July 2021
Problem
For all positive integers define the function
to output
For example,
,
, and
Find the last three digits of
Solution
Notice that ,
,
, and
ends in
for all
. So, the last 3 digits of
are the last
digits of
, which are
.
~Mathdreams