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Prove it

Find condition for which the given series is convergent or divergent

$$\large{\displaystyle \sum^{\infty}_{n=0} \frac{a^n}{x^n+n^a}}$$

where $$a\in R^{+}$$

Note by Tanishq Varshney
1 year, 8 months ago

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divergent · 1 year, 8 months ago

Can you explain why? Staff · 1 year, 8 months ago

@Satyajit Mohanty @Pi Han Goh · 1 year, 8 months ago

How is $$a$$ related to $$x$$? · 1 year, 8 months ago

As such no relation is given, a is a constant · 1 year, 8 months ago

Have you tried Limit Comparison Test yet?

EDIT: Yup: it's just LCT. · 1 year, 8 months ago