Simplify? A)n!+(n+1)!/n!

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Answer 1 · 2018-04-18T11:23:17

#color(blue)(n+2)#

I am assuming the expression is:

#(n!+(n+1)!)/(n!)#

Rewriting as:

#(n!)/(n!)+((n+1)!)/(n!)#

#1+((n+1)!)/(n!)#

#(n+1)! =(n+1)(n+1-1)(n+1-2)(n+1-3).......#

# \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \=(n+1)(n)(n-1)(n-2)......#

#n! =n(n-1)(n-2).........#

#:.#

#1+((n+1)(n)(n-1)(n-2)......)/(n(n-1)(n-2).........)#

#1+((n+1)cancel((n))cancel((n-1))cancel((n-2))......)/(cancel(n)cancel((n-1))cancel((n-2)).........)=1+n+1=n+2#

Answer 2 · 2018-04-18T11:25:23

#n+2#

remember that

#n!=n(n-1)(n-2)(n-3)...1#

I assume the question is

#(n!+(n+1)!)/(n!)#

#=(n!+((n+1)n!))/n!#

#=(cancel(n!)[1+(n+1)])/cancel(n!)#

#=n+2#