Can someone help me determinate the nature of the following series? $$ \frac {a^n}{ (1 + tg(\frac{3}{2}) ( 1+tg(\frac {3}{4}) + ... (1 + tg(\frac{3}{2n})) }$$
Calculate the nature of the following series
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$\begingroup$
sequences-and-series
divergent-series
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0Are you looking for the limit of this, or for the limit of the sum of this? – 2017-02-02
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0A sequence or series.? – 2017-02-02
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0Series! I tried Raabe-Duhamel but to no avail. – 2017-02-02
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0Raabe's test is enough. $$\lim_{n\to+\infty}n\tan\left(\frac{3}{2n}\right)=\frac{3}{2}>1$$ ensures that the given series is convergent at $a=1$. The denominator behaves like $n^{3/2}$. – 2017-02-02