(7n+2)! = (7n+2) x (7n+1) x (7n) x (7n?1) x ..... x 2 x 1 ........... = (7n+2) (7n+1) (7n)! Therefore: (7n)! / (7n+2)! = (7n)! / ((7n+2) (7n+1) (7n)!) = 1 / ((7n+2) (7n+1)) (4n+1)! = (4n+1) x (4n) x (4n?1) x ..... x 2 x 1 ........... = (4n+1) (4n)! Therefore: (4n+1)! / (4n)! = (4n+1) (4n)! / 4n! = 4n+1
(7n)!/(7n+2)! ............. 1.2.3. . . .....(7n) --------------------------------------- 1.2.3 ... 7n(7n+1)(7n+2) . cancel out like terms and get . . . 1 ------------------- (7n+1)(7n+2)
(7n+2)! = (7n+2)(7n+1)(7n)(7n-1)...(2)(1) ???????????= (7n+2)(7n+1)(7n)! So, (7n)!/(7n+2)! = 1/[(7n+2)(7n+1)]
Hint: (7n+2)! = (7n+2)(7n+1)(7n)! and (4n+1)! = (4n+1)(4n)!
