Past exam of the mathematics course of the University of Cambridge / 2020 / ia / Paper 1 / 10F / b

Table of contents
- Solution b

Solution

Boundedness of

(z_{n})

makes both real sequences

(x_{n})

and

(y_{n})

bounded. The Bolzano-Weierstrass theorem first gives a subsequence

(z_{n_{j}})

for which

(x_{n_{j}})

converges. Applying it again to

(y_{n_{j}})

gives a subsubsequence for which the imaginary parts also converge. Since convergence of complex numbers is equivalent to convergence of their real parts and imaginary parts, this subsubsequence converges in

C

.

 Ancestors (10)

 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