silnie, oblicz a) 5!:4!+5! b) (n+1)! : (n-1)! proszę o rozpisanie
silnie, oblicz
a) 5!:4!+5!
b) (n+1)! : (n-1)!
proszę o rozpisanie
a) 5! : 4! + 5! = (4!*5) : 4! + 5! =5+5!= 5+1*2*3*4*5=5+120 = 125 5! : (4!+5!) = 4!*5 : [4!(1+5)] = 5/6 [latex]\ dfrac{5!}{4!+5!} = dfrac{4!cdot5}{4!(1+5)} = dfrac{5}{6} [/latex] b) (n+1)! : (n-1)! = [(n-1)! * n * (n+1)] : (n-1)! = n(n+1) = n² + n
a) 5!:4!+5! = (4!*5):4!+5! = 5+5! = 5+120 = 125 b) (n+1)! : (n-1)! = [latex] frac{(n+1)!}{(n-1)!} = frac{(n-1)!*n*(n+1)}{(n-1)!} = n*(n+1) = n^{2}+n[/latex]