What is the smallest integer a > 0 such that the inequality
1/n + 1
+
1/n + 2
+...+
1/2n + 1
< a - 2010-
1/3
is satisfied for all positive integers n?
Choose the correct choice from the following
A) 2011
B) 2012
C) 2013
D) 2014
E) 2015
Plugging in n = 1, we see that a &gt; 2011. On the other hand, since there are n + 1   terms, and all of them are at most 1=(n + 1), the expression is at most 1, which means that   a = 2012 works.   correct answer 2012
<result>B</result>
What is the smallest integer a > 0 such that the inequality
1/n + 1
+
1/n + 2
+...+
1/2n + 1
< a - 2010-
1/3
is satisfied for all positive integers n?