Question

Efetue. 1/n!-1/(n+1)!

Answer 1

Seja E a expressão dada:

$E=\dfrac{1}{n!}-\dfrac{1}{(n+1)!}\\\\ E=\dfrac{1}{n!}-\dfrac{1}{(n+1)\cdot n!}\\\\ E=\dfrac{n+1}{(n+1)\cdot n!}-\dfrac{1}{(n+1)\cdot n!}\\\\ E=\dfrac{n+1}{(n+1)!}-\dfrac{1}{(n+1)!}\\\\ E=\dfrac{(n+1)-1}{(n+1)!}\\\\ \boxed{E=\dfrac{n}{(n+1)!}}$