Hi, Im having trouble finding the limit as n goes to infiniti of ((n+1)(n+2))/(2n^2). Can someone please help me start this problem?
Your expression is (n+1)(n+2)/2n^2. It's equal to (n^2+3n+2)/2n^2. When you have this, factorize by the variable of the major exponent. In this case it's n^2. So we get (n^2(1+3/n+2/n^2)/(n^2*(2)). Simplify the numerator with the denominator. We get (1+3/n+2/n^2)/2. As n tends to positive infinite, the expression tends to 1/2.
This is usally the method teached before to learn l'Hôpital rule.
limit at infinity :
if deg(numerator)>deg(denominator) -> tends to infinity (sign is to determine with the coefficient of the highest power)
if deg(denominator)>deg(numerator) -> tends to 0
if deg(denominator)=deg(numerator) -> tends to the quotient of the two coefficients corresponding to the highest powers.
First I look the expression to look if there is any indetermination. If there is one like in our example, mindly I do the quotient of the variable afected by the major degree taking in count the coefficients. If I have to answer on paper, I do all the steps.