Give an example limn→∞an=+∞,limn→∞bn=+∞ and limn→∞(an+bn)=−∞.
I think it's impossible, but my teacher says it's real
Answer
If limn→∞an=+∞ and limn→∞bn=+∞, then there is N∈N such that
an,bn>0 for n>N. Therefore an+bn>0 for n>N.
Hence we can not have that limn→∞(an+bn)=−∞.
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