Problem: What is the smallest positive odd integer n such that the product
21/723/7⋯2(2n+1)/7
is greater than 1000?
Answer Choices:
A. 7
B. 9
C. 11
D. 17
E. 19
Solution:
Since 21/7⋯2(2n+1)/7=2(n+1)2/7 and 210=1024, we consider values of n for which (n+1)2/7 is approximately 10 :
2(7+1)2/7=29+71​<2921/2<1000<210<2(9+1)2/7
and n=9.