Скачать или смотреть 1.11 Sum of 1/(n^3 + 1) | Comparison Test | Test of Series | Engineering Mathematics | B.Tech

This lecture is a part of a lecture series given by Mr. Manjeet Singh on Engineering Mathematics for Engineering students at Binary Institute.
Description
1.11 Sum of 1/(n³ + 1) | Comparison Test | Test of Series | Engineering Mathematics | B.Tech

In this video, we solve an important example using the Comparison Test from the topic Test of Series in Engineering Mathematics. The problem discussed in this lecture is the convergence of the infinite series whose general term is 1 divided by (n cube plus 1).

This type of question is commonly asked in B.Tech semester examinations and helps students understand how convergence tests are applied to determine whether a given infinite series converges or diverges.

In this lecture, you will learn:

• How to analyze the series whose general term is 1 divided by (n cube plus 1)
• How to choose an appropriate comparison series
• Step-by-step application of the Comparison Test
• Relationship with the p–series
• Final conclusion about the convergence of the given series

For large values of n, the expression n cube plus 1 behaves very similar to n cube. Therefore, the given series can be compared with the series whose general term is 1 divided by n cube. Since this comparison series is a p-series with power greater than 1, it is convergent. Hence, by the Comparison Test, the given series is also convergent.

This lecture is very helpful for B.Tech students studying Engineering Mathematics, especially those preparing for unit tests, assignments, and semester examinations.

If you want to understand how to solve convergence problems of infinite series step by step using the Comparison Test, this video will help you strengthen your concepts.

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