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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

Respuesta :

LammettHash
[tex]\dfrac34+\dfrac78+\dfrac{11}{12}+\dfrac{15}{16}+\cdots=\displaystyle\sum_{n=1}^\infty\frac{4n-1}}{4n}[/tex]

The [tex]n[/tex]th term in the series is

[tex]\dfrac{4n-1}{4n}=1-\dfrac1{4n}[/tex]

which means for large [tex]n[/tex], the series behaves asymptotically similar to the series

[tex]\displaystyle\sum_{n=1}^\infty1[/tex]

which diverges, so the answer is (B).

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