Question

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

A) The Series Given is n/n+1, where n is the natural number

B)The series is divergent

C)The series is n+4/s +4 times the sequence, where S and N are natural numbers

D)The series is Convergent

Answer 1

`\frac34+\frac78+(11)/(12)+(15)/(16)+\cdots=\displaystyle\sum_(n=1)^\infty\frac{4n-1}}{4n}`

The
`n`th term in the series is


`(4n-1)/(4n)=1-\frac1{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).