How would you prove the following?

Question

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

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Answer 1 · 2017-12-08T03:53:56

See below

To prove: #1/((n-1)!) = n/(n!)#

RHS #= n/(n!)#

# = n/(n*(n-1)*(n-2) .... *2*1)#

# = (1canceln)/(canceln*(n-1)*(n-2) .... *2*1)#

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

#= # LHS