Question

iro ha 2. Show me what you know about bounded sequences! a) What does it mean for a sequence to be bounded? Clearly state the definition using full sentences. A good start is, "A sequence {an) is bounded if and only if..." fra 10 b) Tell me in your own words what it means for a sequence to be bounded. Explain it as though I don't already know what this means, and you are teaching me. :) Ty

Answer 1

fan} 2. a) A sequence is bounded it and only it there exists a BME IR such that I anleM & MEIN. b). Sequence z ons is bounded if it is bounded below and bounded above. Bounded below means it all. terms are number Me, which is called lower Gound of the sequence. an 7 Mi its greater than or equal to a nce is bounded above means equals to which is called the A sequena less it all of its termes are a number M, that or upper bound of the sequence. an < M₂ are 07 an erca you take Therefore all terms in the sequence between M, and M₂ M, – an EM, VnEIN. clear you , It will be very canple. let's take şan} = {5,5,....). It is bounded. The sequence is bounded below by 5 and bounded above by 5. Toke, j'any y-1, 0, 1,-1,0,1, This is bounded, bounded below by / and bounded above by 1, -1 Lan El VnGIN.