Difference between revisions of "1966 IMO Problems/Problem 4"
Line 24: | Line 24: | ||
== See Also == | == See Also == | ||
+ | {{IMO box|year=1966|num-b=3|num-a=5}} |
Revision as of 11:53, 29 January 2021
Problem
Prove that for every natural number , and for every real number
(
;
any integer)
Solution
Assume that is true, then we use
and get
.
First, we prove
LHS=
Using the above formula, we can rewrite the original series as
Which gives us the desired answer of
See Also
1966 IMO (Problems) • Resources | ||
Preceded by Problem 3 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 5 |
All IMO Problems and Solutions |