{xn} is a bounded sequence such that all convergent subsequences converge to the same number

Q: 1 Prove that if a sequence {a„} converges to a, then the sequence {[an]} converges to |a|. Find…

A: Suppose {an} converges to a. Prove that an converges to a. Also, check the converse is true.

Q: B. Prove Bolzano-Weierstrass Theorem. a bounded sequence of real numbers has a convergent…

A: We have to prove

Q: п — 3 - an

A:

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.