F flakine Junior Member Joined Aug 24, 2005 Messages 78 Jul 16, 2006 #1 If converge, find limit: (n+2)!/n! The answer is (n+2)(n+1), diverges. But how did they get the answer??? These types of problems are difficult to understand, can someone help?
If converge, find limit: (n+2)!/n! The answer is (n+2)(n+1), diverges. But how did they get the answer??? These types of problems are difficult to understand, can someone help?
G galactus Super Moderator Staff member Joined Sep 28, 2005 Messages 7,203 Jul 16, 2006 #2 I assume you know what a factorial is. Look at it this way: \(\displaystyle \frac{(n+2)(n+1)n(n-1)(n-2)...........}{n(n-1)(n-2)............}\) Cancel: \(\displaystyle \frac{(n+2)(n+1)\sout{n}\sout{(n-1)}\sout{(n-2)}............}{\sout{n}\sout{(n-1)}\sout{(n-2)}.............}\) That leaves you with: \(\displaystyle (n+2)(n+1)\)
I assume you know what a factorial is. Look at it this way: \(\displaystyle \frac{(n+2)(n+1)n(n-1)(n-2)...........}{n(n-1)(n-2)............}\) Cancel: \(\displaystyle \frac{(n+2)(n+1)\sout{n}\sout{(n-1)}\sout{(n-2)}............}{\sout{n}\sout{(n-1)}\sout{(n-2)}.............}\) That leaves you with: \(\displaystyle (n+2)(n+1)\)
