Problem: Let T=3−8​1​−8​−7​1​+7​−6​1​−6​−5​1​+5​−21​; then
Answer Choices:
A. T<1
B. T=1
C. 1<T<2
D. T>2
E. T=(3−8​)(8​−7​)(7​−6​)(6​−5​)(5​−2)1​
Solution:
By rationalizing the denominator of each function, we see
T=(3+8​)−(8​+7​)+(7​+6​)−(6​+5​)+(5​+2)=3+2=5