(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I know that the statements: if lim sup|s_n|=5, then s_n is bounded, and if lim sup s_n = 0 then lim sup |s_n| are false but I can't think of counter examples? Can someone suggest one or two please. many thanks

2. consider the sequence s_n convergent. Define a new sequence t_n such that

t_n = s_n + (-1)^(n)*(s_n)

a. show that t_n diverges

well lim sup s_n = s

then t_n = s_n*(1 + (-1)^n)

and finally

1/s * lim sup t_n = lim (1+(-1)^n)

the last sequence diverges because no matter how big n gets

the set will be {0, 2/s, 0, 2/s, 0, 2/s} at some point.

b) show by any method that t_n has a convergent subsequence

if we look at the previous tail we see that the 2k terms of n give a convergent subsequence that is

{0,0,0,0..}

right?

thansk!

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# Quick sequence questions

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