Mathematics: 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

Select the true statement about the series, ¾ + 7/8

juli8350

02.01.2022

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

The

th term in the series is

$\dfrac{4n-1}{4n}=1-\dfrac1{4n}$

which means for large

, the series behaves asymptotically similar to the series

$\displaystyle\sum_{n=1}^\infty1$

which diverges, so the answer is (B).

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dward5823

15.02.2020

2,400x3 square meters=7,200 square meters

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