isi-entrance 2016 Q54

isi-entrance · India · UGA 4 marks Sequences and Series Estimation or Bounding of a Sum
For any $n \geq 5$, the value of $1 + \frac{1}{2} + \frac{1}{3} + \cdots + \frac{1}{2^n - 1}$ lies between
(A) 0 and $\frac{n}{2}$
(B) $\frac{n}{2}$ and $n$
(C) $n$ and $2n$
(D) none of the above
For any $n \geq 5$, the value of $1 + \frac{1}{2} + \frac{1}{3} + \cdots + \frac{1}{2^n - 1}$ lies between\\
(A) 0 and $\frac{n}{2}$\\
(B) $\frac{n}{2}$ and $n$\\
(C) $n$ and $2n$\\
(D) none of the above