limn→∞(1+3n)n
What are the general rules for limit of this kind, like limn→∞(1+αn)n or limn→∞(1+αβn)n
And how can I solve this?
Answer
Notice, we know that limn→∞(1+1n)n=e
General rule: let αβn=1t⟹n=αβt
hence, we get limn→∞(1+αβn)n=limt→∞(1+1t)αβt
=(limt→∞(1+1t)t)αβ
=eαβ
No comments:
Post a Comment