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1. n!(n+2)=n!+(n+1)! solve
n!(n+2) = n!+(n+1)! R.H.S = n!+(n+1)! = n!+(n+1)n! = n!(1+n+1) = n!(n+2) = L.H.S HENCE PROVED.
here we have n![ n+2] = n! +[n+1]! here we write [n+1]! as n!. [n+1] n![n+2] = n! + [n+1].n! n!.[n+2] = n![n+1+1] n! [n+2] = n![n+2] here we obtain n+2 =n+2 so its true for all positive intezers you can check this by putting the values
here we have n![ n+2] = n! +[n+1]!
here we write [n+1]! as n!. [n+1]
n![n+2] = n! + [n+1].n!
n!.[n+2] = n![n+1+1]
n! [n+2] = n![n+2]
here we obtain n+2 =n+2
so its true for all positive intezers
you can check this by putting the values
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