hi, i dont understand how to do this limit, for n→∞
d) (n+12n+1)2n
divide numerator and denominator by n, to get (1+n12+n1)2n clearly inside the bracket goes to 2, power increases thus limit doesn't exist (tends to infinity)
divide numerator and denominator by n, to get (1+n12+n1)2n clearly inside the bracket goes to 2, power increases thus limit doesn't exist (tends to infinity)
ah okay thats one good easier way of doing it, could you help me understand where the mark scheme did it?
they proved n+12n+1 was bigger than 3/2 for all n > 0 some how then said (3/2)^2n = (9/4)^n has no limit since 9/4 bigger than 1
ah okay thats one good easier way of doing it, could you help me understand where the mark scheme did it?
they proved n+12n+1 was bigger than 3/2 for all n > 0 some how then said (3/2)^2n = (9/4)^n has no limit since 9/4 bigger than 1
i dont get this
So what they do is that because, for all n>0 , a_n=(3/2)^(2n) < b_n=((2n+1)/(n+1))^(2n) this means that lim n to infinity of a_n < lim n to infinity of b_n which means that as lim a_n goes to infinity, that also lim b_n must also go to infinity.
So what they do is that because, for all n>0 , a_n=(3/2)^(2n) < b_n=((2n+1)/(n+1))^(2n) this means that lim n to infinity of a_n < lim n to infinity of b_n which means that as lim a_n goes to infinity, that also lim b_n must also go to infinity.
I have been forced to use another much time consuming method throughout most of my last two years of highschool, but at the end of my last year I found out about this formula and thought about the amount of time I had spent for nothing xdddd