Difference between revisions of "2014 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 7"
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Revision as of 23:45, 7 November 2014
Problem
Let be a natural number. Show that the sum of the
powers of the first
positive
integers is a polynomial of degree
, i.e.,
,
where
is a polynomial of degree
. For example, for
we have
hence
Solution
See also
2014 UNM-PNM Contest II (Problems • Answer Key • Resources) | ||
Preceded by Problem 6 |
Followed by Problem 8 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
All UNM-PNM Problems and Solutions |