Let {Un} be a sequence of real numbers such that limn→∞ Un exists, then

1
limn→∞ U2n does not exist but limn→∞ U2n+1 exists
2
both limn→∞ U2n and limn→∞  U2n+1 exist
3
both limn→∞ U2n and limn→∞ U2n+1 do not exist
4
limn→∞ U2n exists but limn→∞ U2n+1 does not exist

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