Use the following steps to prove that the sequence xn has no convergent subsequences if and only if ix n i + 00 as n + 00. a) suppose that the sequence xn has no convergent subsequences. let m > o. prove that there exist at most finitely many values of n such that xn e [-m, m]. explain why this implies ixn i + 00 as n + 00. b) suppose ixn i + 00 as n + 00. show that xn has no convergent subsequence. (hint: exercise 1.61 may .)

step-by-step explanation:

step-by-step explanation:

given that there are two triangles j'k'l' and jkl>

the former is got by dilating the second one.

when drawn on a grid, (graph paper) coordinates of vertices of first triangle is

(6,12)j, (9,6)k and (12,9)l

side jk has length = distance between j and k

=

side j'k'=distance between j' and k'

=

ie j'k'l' has sides 1/3 of that of corresponding sides of jkl.

hence scale factor of 1/3 is used to get j'k'l'from jkl

i'm pretty sure the answer is a. decreases with increase in