2021 JMPSC Invitationals Problems/Problem 4
Contents
[hide]Problem
Let and
be sequences of real numbers such that
,
, and, for all positive integers
,
Find
.
Solution
We notice that
Since we are given that
and
, we can plug these values in to get that
Similarly, we conclude that
Adding and
gives us
Dividing both sides by
yields
~mahaler
Solution 2
Add both equations to get , and subtract both equations to get
, so now we bash:
and
.
and
.
and
.
and
,
~Geometry285
See also
- Other 2021 JMPSC Invitationals Problems
- 2021 JMPSC Invitationals Answer Key
- All JMPSC Problems and Solutions
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