Question

Select the true statement about the series, ¾ + 7/8 + 11/12 + 15/16…

Answer 1

$\dfrac34+\dfrac78+\dfrac{11}{12}+\dfrac{15}{16}+\cdots=\displaystyle\sum_{n=1}^\infty\frac{4n-1}}{4n}$

The $n$th term in the series is

$\dfrac{4n-1}{4n}=1-\dfrac1{4n}$

which means for large $n$, the series behaves asymptotically similar to the series

$\displaystyle\sum_{n=1}^\infty1$

which diverges, so the answer is (B).