Find the following limits using L'Hpital's rule (please also write down the detailed steps): n +n+1 In(n) +4 2 5n +7n +6 lim n-00 2n + 3 9 ne" lim- lim- n 2n +3' n lim n1-00 2" " log (n)' n 1.007 lim n-00 nln nln(n)' lim n-00 n 1.99 n +n+1 n ln(n) +n +2 Show, using a proof by induction, that k2=2+(N-1)2N+ N k=0