question set 3

Question

question set 3

anonymous · Answer

attachment

anonymous · Answer

ok shall we start ?

anonymous · Answer

yesss

anonymous · Answer

for a there is a thm abt subset right ?

anonymous · Answer

oh?

anonymous · Answer

the monotone Subsequence thm

anonymous · Answer

its state that :-
if X is a sequence of a real numbers then there is a subsequence of X that is monotone

anonymous · Answer

the one you showed in last question?

anonymous · Answer

nope :O

anonymous · Answer

im sure u can find it ur txt book :O

anonymous · Answer

if i had books on maths
the only material i hv is questions

anonymous · Answer

okay anyway,how do we solve it

anonymous · Answer

wutt ;_;
why u dnt have the book for real analysis :(

anonymous · Answer

-.- because am not major in maths

anonymous · Answer

anyway
$ x_n=x_1+x_2+...x_n $
all possitive
and $x_{n+1} < x_n$

$\sum (-1)^nx_n =-x_1+2x_2-3x_3+4x_4 +....$
$=-(x_1+3x_3+5x_n+...) +(2x_2+4x_4+6x_6+...)$

anonymous · Answer

and?

anonymous · Answer

sry open study  is laging
so what u can see is
 lim $ x_n= (x_1 +x_3+x_5+.. )+(x_2+x_4+x_6+..)$=0
lim $ (x_2+x_4+x_6+..)=- (x_1 +x_3+x_5+.. )$
let
 k= $(x_1 +3x_3+5x_5+..) >  (x_1 +x_3+x_5+.. )$>0
then
$Y_n$second seq
$y_n $=- k +(the even part)
so limit y_n >0
cuz the even part >k
then its bounded + deaceasins
so its convergent monotone

anonymous · Answer

thank you @BSwan  you have been a lovely lifesaver
i will try to solve the rest ^^ they are tiring to type here
hehe 
@}:->-

anonymous · Answer

nope lol im not a life saver :P
i dnt help hehe

anonymous · Answer

come on ^^ you did

anonymous · Answer

no lol 
i dnt help xD
i just enjoy the problems i would like to learn :)
i dnt help ppl on OS :P

anonymous · Answer

hehe