Thursday, 14 July 2016

calculus - Evaluating limlimitsntoinftyleft(1+3overnright)n





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=1tn=αβt
hence, we get limn(1+αβn)n=limt(1+1t)αβt
=(limt(1+1t)t)αβ
=eαβ


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