(FGV - 1973) Uma das afirmações abaixo é falsa. Assinale-a:
a)
$\,n!\,-\,(n\,-\,1)!\,=\,(n\,-\,1)!\centerdot(n\,-\,1)\,$
b)
$\,2(n!)\,-\,(n\,-\,1)!\centerdot(n\,-\,1)\,=$ $\,(n\,-\,1)!\,-\,n!\,$
c)
$\,(n!)^2\,=\,[(n\,+\,1)!\,-\,n!]\centerdot (n\,-\,1)!$
d)
$\,(2n\,+\,1)!\,=\,(2n\,-\,1)!(4n^2\,+\,2n)$
e)
$\,\dfrac{1}{n!}\,-\,\dfrac{1}{(n\,+\,1)!}\,=\,\dfrac{n}{(n\,+\,1)!}\,$
