Direct Comparison Test

Equation
$$0 \leq a_{n} \leq b_{n}$$

Use
Find a series with a known convergence that can easily be compared to the target series.Show that the selected series is either larget or smaller than the known series.If the target series is less than the known series for the whole domain and the known series converges, so does the target series.If the known series diverges and the target series is larger than the known series, the target series will definetely diverge. 

Explanation
If $$a_{n}$$ and $$b_{n}$$ are infinite series where the known series  $$b_n$$ converges absolutely, if we can prove that for all real numbers $$|a_n| \leq |b_n|$$ then through the squeeze theorum we can say that $$\lim_{n \rightarrow oo} a_n$$ exists and is less than $$\lim_{n \rightarrow oo} b_n$$.

Video Explanation


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