Problem: In the expansion of (a−a1)7 the coefficient of a−1/2 is:
Answer Choices:
A. −7
B. 7
C. −21
D. 21
E. 35
Solution:
(a−a1/21)7=a7−7a1/2+21a4−21a3/2+35a−21a−1/2+7a−2−a−7/2
(r+1) th term =(r7)a7−r(−a−1/2)r=±(r7)a7−r−r/2. We need a7−r−r/2=a−1/2,7−23r=−21,r=5
∴6 th term =1⋅2⋅3⋅4⋅57⋅6⋅5⋅4⋅3a2(−a)−5/2=−21a−1/2.