Friday, 13 January 2017

limits - Evaluating limntoinftyleft(fracn+3n+1right)2n



I am having a hard time finding the next step on this.



Can someone tell me what is the next step and explain to me
in non-mathematical terms what I am supposed to do when I reach

this examples at this place ?



limn(n+3n+1)2n=limn(n+1+2n+1)2n=limn(1+2n+1)2n=limn(1+2n+1)?


Answer



limn(n+3n+1)2n=limn(n(1+3n)n(1+1n))2n=limn((1+3n)(1+1n))2n=limn((1+3n)n)2((1+1n)n)2=

=(e3)2(e1)2=e6e2=e62=e4.



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