Calculus 2, Lec 23D: Comparison Test to Prove ∑1/(n^3+1) Converges
In math analysis and calculus, the Comparison Test for convergence and divergence of infinite series is very useful for proofs. In this video, we compare the series ∑1/(n^3+1) with the p-series ∑1/n^3. For the sequences of terms, we have a_n = 1/(n^3+1) and b_n = 1/n^3. The inequalities 0 ≤ a_n ≤ b_n are true for all positive integer values of n. Since ∑b_n = ∑1/n^3 converges, being a p-series with p = 3, which is strictly greater than 1, the Comparison Test now implies that the series ∑a_n = ∑1/(n^3+1) converges. This is the proof.
#Calculus2 #ComparisonTest #apcalculusbc
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