Question

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

A: The series is given by n/n+1 , where n is a natural number.
B: The series is divergent
C: The series is n+4s+4 times the sequence, where n and s are natural numbers
D: The series is convergent

Answer 1

`\frac34+\frac78+(11)/(12)+(15)/(16)+\cdots=\displaystyle\sum_(n\ge1)(4n-1)/(4n)`

We have


`\displaystyle\lim_(n\to\infty)(4n-1)/(4n)=\frac44=1\\eq0`

which means the sum diverges.