Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2024 / Paper 1 / 19 / c / ii

Table of contents
- Solution ii

Solution

Compare the positive terms with those of the harmonic series:

\frac{( n ^{2} + 2 n ) / ( n ^{3} + 3 n ^{2} + 1 )}{1/ n} = \frac{n ^{3} + 2 n ^{2}}{n ^{3} + 3 n ^{2} + 1} ⟶ 1.

By the limit comparison test, the given series has the same convergence behaviour as

\sum 1/ n

, which diverges. Thus the series diverges to $+ \infty$ .

 Ancestors (13)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version