Problem:
1+2+31​1​1​=
Answer Choices:
A. 61​
B. 103​
C. 107​
D. 65​
E. 310​
Solution:
Using the common denominators and simplifying yield
1+2+31​1​1​=1+37​1​1​=1+73​1​=710​1​=107​
OR
Clearing fractions and simplifying yield
1+(2+31​)×31×3​1​=1+6+13​1​=(1+73​)×71×7​=7+37​=107​
OR
Estimating, the result is between
1+21​1​=23​1​=32​ and 1+31​1​=34​1​=43​
The only choice in this interval is 107​.
Answer: C​.
The problems on this page are the property of the MAA's American Mathematics Competitions