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Is it true that for any bounded sequences (sn) and (tn), limsup(sn +tn)=limsupsn +limsuptn ? If...

Is it true that for any bounded sequences (sn) and (tn),
limsup(sn +tn)=limsupsn +limsuptn ?
If the statement is true, give a proof. If it is false, give a counterexample.
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