For school, I need to solve the following two problems:
1.) Prove, without calculator/computer, that 2010^2008<2009^2009<2008^2010.
I believe using (n+1)^(n-1)<n^n<(n-1)^(n+1) then taking the ln of all three is the way to go.
2.) Find the limit as n goes to infinity of 1/n*sqrt[(5n)!/(3n)!] the answer for this one is NOT 0.
*Anyone that has the time and kindness PLEASE help me out. Thank you very much. And the answers do not require anything past Calculus II (integrals/limits etc)