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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

Respuesta :

LammettHash
[tex]\dfrac34+\dfrac78+\dfrac{11}{12}+\dfrac{15}{16}+\cdots=\displaystyle\sum_{n\ge1}\frac{4n-1}{4n}[/tex]

We have

[tex]\displaystyle\lim_{n\to\infty}\frac{4n-1}{4n}=\dfrac44=1\neq0[/tex]

which means the sum diverges.

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