2021 JMPSC Sprint Problems/Problem 20
For all integers and , define the operation as Find
Let . Then, and . We substitute these values into expression to get Recall the definition for the operation ; using this, we simplify our expression to We have and , so we can expand the numerator of the fraction within the square root as to get ~samrocksnature
Basically the same as above, but instead we can let . Then we have
which equals .
, , and .
The problems on this page are copyrighted by the Junior Mathematicians' Problem Solving Competition.