Can someone help me determinate the nature of the following series? $$ \frac {a^n}{ (1 + tg(\frac{3}{2}) ( 1+tg(\frac {3}{4}) + ... (1 + tg(\frac{3}{2n})) }$$
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Are you looking for the limit of this, or for the limit of the sum of this? – N. S. Feb 02 '17 at 19:06
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A sequence or series.? – Nosrati Feb 02 '17 at 19:06
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Series! I tried Raabe-Duhamel but to no avail. – Eduard6421 Feb 02 '17 at 19:08
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Raabe'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 $n^{3/2}$. – Jack D'Aurizio Feb 02 '17 at 19:10