Question

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

Answer 1

$\dfrac34+\dfrac78+\dfrac{11}{12}+\dfrac{15}{16}+\cdots=\displaystyle\sum_{n\ge1}\frac{4n-1}{4n}$

We have

$\displaystyle\lim_{n\to\infty}\frac{4n-1}{4n}=\dfrac44=1\neq0$

which means the sum diverges.